diff --git a/backend/src/app.ts b/backend/src/app.ts
index 9f06e67..469b3c3 100755
--- a/backend/src/app.ts
+++ b/backend/src/app.ts
@@ -20,6 +20,7 @@ import customersRouter from './routes/customers';
 import passkeysRouter from './routes/passkeys';
 import passkeyLoginRouter from './routes/passkeyLogin';
 import googleAuthRouter from './routes/googleAuth';
+import { googleConfig } from './google/config';
 import publicRouter from './routes/public';
 import cartRouter from './routes/cart';
 import shippingAddressesRouter from './routes/shippingAddresses';
@@ -72,7 +73,16 @@ app.get('/api/config', (_req, res) => {
     // keeps QA out of production's Brevo account: QA sets no key, so no QA
     // browsing is ever reported, and there is no flag anyone can forget to
     // turn off. Same shape as paypalClientId above.
-    brevoTrackerKey: process.env.BREVO_TRACKER_KEY?.trim() || null
+    brevoTrackerKey: process.env.BREVO_TRACKER_KEY?.trim() || null,
+    // Whether to offer the Google button at all (#345). A boolean, never the
+    // client id: the browser does not need it, because the whole flow is a
+    // redirect this server builds.
+    //
+    // Absent rather than disabled is the point. A developer with no credentials
+    // gets a storefront that works and simply does not offer the option, the
+    // same choice #41 made for a browser without WebAuthn — and QA, which
+    // cannot have credentials until #313, gets the same.
+    googleSignIn: googleConfig().enabled
   });
 });
 
diff --git a/backend/tests/integration/googleSignIn.integration.test.ts b/backend/tests/integration/googleSignIn.integration.test.ts
index de0bae2..0c7f16f 100644
--- a/backend/tests/integration/googleSignIn.integration.test.ts
+++ b/backend/tests/integration/googleSignIn.integration.test.ts
@@ -730,3 +730,54 @@ describe('GET /api/customers/me/identities', () => {
     expect(res.status).toBe(401);
   });
 });
+
+/**
+ * Whether the storefront offers a Google button at all (#345).
+ *
+ * A boolean and never the client id: the browser does not need one, because
+ * the whole flow is a redirect the server builds.
+ */
+describe('GET /api/config, google sign-in', () => {
+  // The suite-wide beforeEach configures Google so the flow above can run.
+  // These tests are about the unconfigured case too, so they start from clean.
+  beforeEach(() => {
+    delete process.env.GOOGLE_CLIENT_ID;
+    delete process.env.GOOGLE_CLIENT_SECRET;
+  });
+
+  it('is false when the environment has no credentials', async () => {
+    const res = await request(app).get('/api/config');
+
+    // Which is the state of local development, and of QA until #313 moves it
+    // off a hostname whose domain nobody can prove they own.
+    expect(res.body.googleSignIn).toBe(false);
+  });
+
+  it('is true when both credentials are set', async () => {
+    process.env.GOOGLE_CLIENT_ID = 'id.apps.googleusercontent.com';
+    process.env.GOOGLE_CLIENT_SECRET = 'shh';
+
+    const res = await request(app).get('/api/config');
+
+    expect(res.body.googleSignIn).toBe(true);
+  });
+
+  it('is false with only one of the pair, matching what the backend refuses to boot on', async () => {
+    process.env.GOOGLE_CLIENT_ID = 'id.apps.googleusercontent.com';
+
+    const res = await request(app).get('/api/config');
+
+    expect(res.body.googleSignIn).toBe(false);
+  });
+
+  it('never sends the client id or secret to the browser', async () => {
+    process.env.GOOGLE_CLIENT_ID = 'id.apps.googleusercontent.com';
+    process.env.GOOGLE_CLIENT_SECRET = 'a-real-looking-secret';
+
+    const res = await request(app).get('/api/config');
+
+    const body = JSON.stringify(res.body);
+    expect(body).not.toContain('a-real-looking-secret');
+    expect(body).not.toContain('googleusercontent');
+  });
+});
diff --git a/docs/ops/google-sign-in.md b/docs/ops/google-sign-in.md
new file mode 100644
index 0000000..ad603f8
--- /dev/null
+++ b/docs/ops/google-sign-in.md
@@ -0,0 +1,106 @@
+# Google sign-in
+
+What has to be true outside the repository for the Google button to work, and
+what to do at the domain cutover. The code side is #332 and the six issues under
+it; this is only the parts that live in a browser tab at Google.
+
+## Where it is configured
+
+The **Google Auth Platform** in the Google Cloud Console, in one project. There
+is one consent screen per project and every OAuth client in it shares that
+screen, so what appears there is the production identity even while testing.
+
+| Section | What it holds |
+| --- | --- |
+| Branding | App name, support email, authorized domains, the three app links |
+| Audience | External, publishing status, test users |
+| Clients | The OAuth client, its redirect URIs, the id and secret |
+| Data Access | Exactly `openid`, `email`, `profile` |
+| Verification Center | Nothing to submit, and it should stay that way |
+
+## The constraint that shapes everything
+
+**Google refuses a redirect URI whose host is not under an authorized domain,
+and a domain can only be authorized after ownership is proved by DNS in Search
+Console.** `localhost` is the only exemption.
+
+`qa-redefined-designs.bermudalamb.synology.me` therefore cannot ever be used:
+Synology owns the registrable domain above it, so there is no record to add and
+nothing to prove. This is the same wall #285 hit with Cloudflare.
+
+The consequence, stated plainly because it changes how the feature is worked on:
+
+| Environment | Google sign-in |
+| --- | --- |
+| Local, on `localhost` | Works, by exemption |
+| QA on the Synology hostname | **Impossible**, not merely unconfigured |
+| QA on `qa.redefined-designs.com` | Works, after the cutover |
+| Production on `redefined-designs.com` | Works, after the cutover |
+
+So this feature is built and exercised locally, and QA cannot see it at all
+until QA moves onto a subdomain of the real domain. The Search Console property
+for `redefined-designs.com` already covers `qa.redefined-designs.com`, because
+a Domain property covers every subdomain.
+
+`docker-compose.qa.yml` sets both credentials to empty deliberately, with a
+comment saying so, and the storefront then offers no button rather than one that
+fails at Google.
+
+## Scopes, and why publishing needs no review
+
+`openid` produces the id token carrying the subject claim, which is the identity
+stored. `email` carries the address and the `email_verified` flag the linking
+policy turns on. `profile` carries the names used when an account is created.
+
+All three are non-sensitive. Requesting only them is what lets the app publish
+without verification and without customers seeing an unverified-app warning.
+**Add one sensitive scope and publishing becomes a review with a video
+walkthrough and a wait measured in weeks.** Nothing in this feature needs one.
+
+Uploading an app logo also triggers a brand review, which is why Branding has
+none.
+
+## The cutover checklist, for #313
+
+1. Point QA at `qa.redefined-designs.com` and set its `PUBLIC_URL` to match.
+2. Set `GOOGLE_CLIENT_ID` and `GOOGLE_CLIENT_SECRET` in the QA stack. Both or
+   neither — the backend refuses to start on one without the other, because the
+   failure would otherwise arrive the moment a customer presses the button.
+3. In **Clients**, add the QA callback:
+   `https://qa.redefined-designs.com/api/auth/google/callback`
+4. Confirm the production callback is registered:
+   `https://redefined-designs.com/api/auth/google/callback`
+5. In **Audience**, move the publishing status from Testing to **In production**.
+   Do it once the domain resolves, so the home page and privacy links Google
+   shows actually answer.
+
+No code changes at any step. The redirect URI is derived from `PUBLIC_URL`, so
+the environment variable and the console entry are the whole of it.
+
+**Leaving it in Testing is the failure to watch for.** Only listed test users can
+sign in, and the refusal happens on Google's own page, so nothing reaches the
+storefront and nothing appears in its logs. A customer reports a broken button
+and the logs are silent.
+
+## The production smoke test
+
+The consent screen, the redirect and the domain are all environment-specific, so
+QA proves the flow and not the configuration. After the cutover:
+
+1. Sign in with a Google account that has never been used on the site. A new
+   customer is created and lands on the consent step.
+2. Sign in again with the same account. It reaches the same customer rather than
+   a second one.
+3. Check the account page lists Google under connected accounts.
+
+## What is not offered, and why
+
+**Unlinking.** A customer cannot detach their Google account. Removing the only
+way into an account is guarded for passkeys and the same guard would be needed
+here first. Worth its own issue when somebody actually asks.
+
+**Apple.** A separate decision with a materially different cost, set out on
+#332: a paid developer programme, a client secret that expires every six months,
+no `localhost` redirect URIs at all, and a name and email returned exactly once.
+Apple is required for iOS apps offering third-party sign-in, and this is a
+website, so that rule does not apply here.
diff --git a/frontend/src/api.ts b/frontend/src/api.ts
index 1463440..8a92414 100755
--- a/frontend/src/api.ts
+++ b/frontend/src/api.ts
@@ -61,6 +61,14 @@ export interface SiteConfig {
    * A key alone does not start tracking — see brevo.ts.
    */
   brevoTrackerKey: string | null;
+  /**
+   * Whether Google sign-in is configured in this environment (#345).
+   *
+   * False locally without credentials, and false in QA until #313 moves it off
+   * the Synology hostname — Google refuses a redirect URI whose domain nobody
+   * can prove they own. The button is then absent rather than disabled.
+   */
+  googleSignIn: boolean;
 }
 
 export async function fetchConfig(): Promise<SiteConfig> {
diff --git a/frontend/src/customer/AuthForm.tsx b/frontend/src/customer/AuthForm.tsx
index b70a598..b357f35 100644
--- a/frontend/src/customer/AuthForm.tsx
+++ b/frontend/src/customer/AuthForm.tsx
@@ -1,4 +1,4 @@
-import { useState } from 'react';
+import { useEffect, useState } from 'react';
 import { useSearchParams } from 'react-router-dom';
 import Form from 'antd/es/form';
 import Input from 'antd/es/input';
@@ -10,6 +10,8 @@ import Typography from 'antd/es/typography';
 import Divider from 'antd/es/divider';
 import { registerCustomer, loginCustomer, signInWithPasskey, passkeysSupported } from './customerApi';
 import { useCustomerAuth } from './CustomerAuthContext';
+import GoogleSignInButton from './GoogleSignInButton';
+import { fetchConfig } from '../api';
 
 const { Text } = Typography;
 
@@ -42,6 +44,15 @@ type Props = Readonly<{
   // route closes back to the page behind it, while the cart and favorite
   // prompts resume the action the customer was interrupted doing.
   onSuccess: () => void;
+  /**
+   * Where a Google sign-in should return the customer (#345).
+   *
+   * Supplied by the caller because only the caller knows: the route modal has a
+   * page behind it, and the cart prompt has the page it interrupted. An OAuth
+   * redirect leaves the application entirely, so this cannot be recovered
+   * afterwards the way onSuccess recovers it for every other path.
+   */
+  returnTo?: string;
 }>;
 
 /**
@@ -73,7 +84,7 @@ function googleNotice(reason: string | null): string | null {
 // written twice — once as the /login and /register pages, once inside the
 // prompt shown when a signed-out visitor adds to the cart — which had already
 // drifted in consent wording and in which links each offered.
-export default function AuthForm({ mode, onModeChange, onForgotPassword, onSuccess }: Props) {
+export default function AuthForm({ mode, onModeChange, onForgotPassword, onSuccess, returnTo = '/' }: Props) {
   const [searchParams] = useSearchParams();
   const notice = googleNotice(searchParams.get('auth'));
   const [error, setError] = useState<string | null>(null);
@@ -89,6 +100,20 @@ export default function AuthForm({ mode, onModeChange, onForgotPassword, onSucce
   // rather than whether pressing it works.
   const canUsePasskeys = passkeysSupported();
 
+  // Whether this environment has Google credentials at all. Fetched rather than
+  // built in, because one image serves every environment — and false is the
+  // right starting value: a button that appears a moment late is better than
+  // one that appears and then vanishes.
+  const [googleEnabled, setGoogleEnabled] = useState(false);
+  useEffect(() => {
+    fetchConfig()
+      .then((config) => setGoogleEnabled(config.googleSignIn))
+      // Silent, and the button simply never appears. The password form behind
+      // it works regardless, which is the whole reason it is below rather than
+      // above.
+      .catch(() => setGoogleEnabled(false));
+  }, []);
+
   async function submit(action: () => Promise<unknown>) {
     setLoading(true);
     setError(null);
@@ -238,11 +263,13 @@ export default function AuthForm({ mode, onModeChange, onForgotPassword, onSucce
                     works for everyone. Absent entirely where WebAuthn is not
                     available, rather than shown disabled: a greyed button
                     invites a customer to wonder what they are missing (#41). */}
+                {(canUsePasskeys || googleEnabled) && (
+                  <Divider plain style={{ marginBlock: 16 }}>
+                    <Text type="secondary" style={{ fontSize: 12 }}>or</Text>
+                  </Divider>
+                )}
                 {canUsePasskeys && (
                   <>
-                    <Divider plain style={{ marginBlock: 16 }}>
-                      <Text type="secondary" style={{ fontSize: 12 }}>or</Text>
-                    </Divider>
                     <Button
                       block
                       loading={passkeyLoading}
@@ -258,6 +285,17 @@ export default function AuthForm({ mode, onModeChange, onForgotPassword, onSucce
                     </Text>
                   </>
                 )}
+                {/* Below the passkey button, which is below the password form.
+                    The order is deliberate and it is not about preference: a
+                    passkey is already on the device in front of the customer,
+                    while Google is a round trip to somebody else's site. Absent
+                    rather than disabled where it is not configured, for the
+                    same reason as the one above (#345). */}
+                {googleEnabled && (
+                  <div style={{ marginTop: canUsePasskeys ? 16 : 0 }}>
+                    <GoogleSignInButton returnTo={returnTo} />
+                  </div>
+                )}
               </Form>
             )
           }
diff --git a/frontend/src/customer/AuthPromptModal.tsx b/frontend/src/customer/AuthPromptModal.tsx
index b1a2fa8..f4439fd 100644
--- a/frontend/src/customer/AuthPromptModal.tsx
+++ b/frontend/src/customer/AuthPromptModal.tsx
@@ -37,6 +37,12 @@ export default function AuthPromptModal({ open, onClose, onSuccess }: Props) {
           onClose();
           navigate('/forgot-password', { state: { background: location } });
         }}
+        // The page the customer was on when this interrupted them, which is
+        // where a Google round trip should put them back (#345). Unlike
+        // onSuccess it cannot resume the interrupted action — the redirect
+        // leaves the application — so it returns them to the page and they
+        // press the button again.
+        returnTo={`${location.pathname}${location.search}`}
         onSuccess={onSuccess}
       />
     </Modal>
diff --git a/frontend/src/customer/AuthRouteModal.tsx b/frontend/src/customer/AuthRouteModal.tsx
index 99575ca..316b44d 100644
--- a/frontend/src/customer/AuthRouteModal.tsx
+++ b/frontend/src/customer/AuthRouteModal.tsx
@@ -7,6 +7,15 @@ type Props = Readonly<{
   // Moving between the auth routes, supplied by the router so the rule about
   // keeping the whole detour to one history entry lives in one place.
   onNavigate: (path: string) => void;
+  /**
+   * The page behind this modal, for a Google sign-in to return to (#345).
+   *
+   * Supplied by the router, which is the only thing that knows it: this modal
+   * renders over a backdrop location, and its own path is /login, so reading
+   * the current URL here would send the customer back to the form they just
+   * left.
+   */
+  returnTo: string;
 }>;
 
 const TITLES: Record<AuthMode, string> = {
@@ -18,7 +27,7 @@ const TITLES: Record<AuthMode, string> = {
 // clicks Log in while browsing and changes their mind is not stranded. Both
 // stay real routes: /reset-password links to /login, and customers may have
 // bookmarks.
-export default function AuthRouteModal({ mode, onClose, onNavigate }: Props) {
+export default function AuthRouteModal({ mode, onClose, onNavigate, returnTo }: Props) {
   return (
     <Modal
       title={TITLES[mode]}
@@ -36,6 +45,7 @@ export default function AuthRouteModal({ mode, onClose, onNavigate }: Props) {
         // in while browsing wants to carry on browsing rather than be moved to
         // their account page.
         onSuccess={onClose}
+        returnTo={returnTo}
       />
     </Modal>
   );
diff --git a/frontend/src/customer/GoogleSignInButton.tsx b/frontend/src/customer/GoogleSignInButton.tsx
new file mode 100644
index 0000000..4ce5d4b
--- /dev/null
+++ b/frontend/src/customer/GoogleSignInButton.tsx
@@ -0,0 +1,68 @@
+import Button from 'antd/es/button';
+
+/**
+ * Google's own mark, inlined as SVG (#345).
+ *
+ * Their identity guidelines specify the four colours and the geometry, and a
+ * hand-drawn approximation of somebody else's trademark is a compliance problem
+ * rather than a style choice. These are the published values.
+ *
+ * Inlined rather than fetched, for the reason every other asset in this app is:
+ * a second origin is a second thing that can be down, blocked, or slow, and
+ * this one sits on the sign-in path.
+ */
+function GoogleMark() {
+  return (
+    <svg width="18" height="18" viewBox="0 0 18 18" aria-hidden="true" focusable="false">
+      <path
+        fill="#4285F4"
+        d="M17.64 9.2c0-.64-.06-1.25-.16-1.84H9v3.48h4.84a4.14 4.14 0 0 1-1.8 2.72v2.26h2.92c1.7-1.57 2.68-3.88 2.68-6.62z"
+      />
+      <path
+        fill="#34A853"
+        d="M9 18c2.43 0 4.47-.8 5.96-2.18l-2.92-2.26c-.8.54-1.84.86-3.04.86-2.34 0-4.32-1.58-5.03-3.7H.96v2.34A9 9 0 0 0 9 18z"
+      />
+      <path
+        fill="#FBBC05"
+        d="M3.97 10.72a5.4 5.4 0 0 1 0-3.44V4.94H.96a9 9 0 0 0 0 8.12l3.01-2.34z"
+      />
+      <path
+        fill="#EA4335"
+        d="M9 3.58c1.32 0 2.5.45 3.44 1.35l2.58-2.59C13.46.9 11.43 0 9 0A9 9 0 0 0 .96 4.94l3.01 2.34C4.68 5.16 6.66 3.58 9 3.58z"
+      />
+    </svg>
+  );
+}
+
+type Props = Readonly<{
+  /** Where to send the customer back to. Validated again on the server. */
+  returnTo: string;
+}>;
+
+/**
+ * Signing in with Google (#345).
+ *
+ * A navigation rather than a fetch, which is what makes this different from
+ * every other control on the auth form. The flow leaves this application
+ * entirely, so there is no promise to await and no error to catch here — the
+ * server's callback decides what happens and redirects accordingly.
+ *
+ * `returnTo` is sent as a query parameter and **validated on the server**, not
+ * here. It has to be, since anyone can type the URL, and doing it in one place
+ * beats doing it in two languages. See `google/returnTo.ts`.
+ */
+export default function GoogleSignInButton({ returnTo }: Props) {
+  return (
+    <Button
+      block
+      icon={<GoogleMark />}
+      onClick={() => {
+        // assign rather than the router: this is a full page departure to
+        // another origin, and react-router would try to match it as a route.
+        window.location.assign(`/api/auth/google/start?returnTo=${encodeURIComponent(returnTo)}`);
+      }}
+    >
+      Sign in with Google
+    </Button>
+  );
+}
diff --git a/frontend/src/main.tsx b/frontend/src/main.tsx
index 87e6142..5b48b6e 100755
--- a/frontend/src/main.tsx
+++ b/frontend/src/main.tsx
@@ -148,6 +148,10 @@ function AppRoutes() {
   // the storefront, so closing always lands somewhere real.
   const background = state?.background;
   const backdrop = modalPath ? background ?? { ...location, ...STOREFRONT_BACKDROP } : location;
+  // Where a Google sign-in should land the customer: the page behind the modal,
+  // not the modal's own path. Built here because the backdrop is only known
+  // here, and validated again on the server (#345).
+  const returnTo = `${backdrop.pathname}${backdrop.search ?? ''}`;
 
   function closeModal() {
     // Back, when there is somewhere to go back to, so closing the modal and
@@ -193,10 +197,10 @@ function AppRoutes() {
         {import.meta.env.DEV && <DevThrow scope="modal" />}
         {modalPath === '/account' && <Account onClose={closeModal} />}
         {modalPath === '/login' && (
-          <AuthRouteModal mode="login" onClose={closeModal} onNavigate={goWithinAuth} />
+          <AuthRouteModal mode="login" onClose={closeModal} onNavigate={goWithinAuth} returnTo={returnTo} />
         )}
         {modalPath === '/register' && (
-          <AuthRouteModal mode="register" onClose={closeModal} onNavigate={goWithinAuth} />
+          <AuthRouteModal mode="register" onClose={closeModal} onNavigate={goWithinAuth} returnTo={returnTo} />
         )}
         {modalPath === '/forgot-password' && (
           <ForgotPassword onClose={closeModal} onBackToSignIn={() => goWithinAuth('/login')} />
diff --git a/frontend/tests/e2e/auth.spec.ts b/frontend/tests/e2e/auth.spec.ts
index e6f51db..2cd733d 100755
--- a/frontend/tests/e2e/auth.spec.ts
+++ b/frontend/tests/e2e/auth.spec.ts
@@ -119,6 +119,30 @@ test.describe('Customer accounts', () => {
     await header.waitForSignedIn();
   });
 
+  // #345. Local development has no Google credentials, and neither does QA
+  // until #313 moves it off a hostname whose domain nobody can prove they own.
+  // So the button being ABSENT is the behaviour under test here, and it is the
+  // one that matters: a control that appears and then fails at Google is worse
+  // than one that was never offered.
+  test('offers no Google button when the environment is not configured for it', async ({
+    authModal,
+    accountModal,
+    customer,
+    header
+  }) => {
+    await accountModal.openAndLogOut();
+    await expect(header.logInButton).toBeVisible();
+    await authModal.gotoLogIn();
+
+    const google = authModal.logInDialog.getByRole('button', { name: /Sign in with Google/i });
+    await expect(google).toHaveCount(0);
+
+    // And the password form is untouched by its absence, which is the whole
+    // reason the alternatives sit below it rather than above.
+    await authModal.logIn(customer.email, customer.password);
+    await header.waitForSignedIn();
+  });
+
   test('rejects login with the wrong password', async ({ page, customer, accountModal, authModal, header }) => {
     await accountModal.openAndLogOut();
     await expect(header.logInButton).toBeVisible();