diff --git a/e2e/pwa.e2e.ts b/e2e/pwa.e2e.ts
index 117991b..85767e0 100644
--- a/e2e/pwa.e2e.ts
+++ b/e2e/pwa.e2e.ts
@@ -165,6 +165,19 @@ test.describe('the version link', () => {
 });
 
 test.describe('offline', () => {
+  test('says the site is ready to work offline once the first load has cached it, and not on later loads', async ({ page }) => {
+    await withSite(async (site) => {
+      await openAt(page, site);
+
+      await expect(page.locator('#offline-status')).toHaveText('Ready to work offline.', { timeout: RESULT_TIMEOUT_MS });
+
+      await page.reload();
+      await new Explorer(page).ready();
+
+      await expect(page.locator('#offline-status')).toHaveText('');
+    });
+  });
+
   test('opens, runs an operation and shows the engine with no network once it has been loaded', async ({ page }) => {
     await withSite(async (site) => {
       const explorer = await controlledPage(page, site);
diff --git a/site/index.html b/site/index.html
index 2424f4b..9838d19 100644
--- a/site/index.html
+++ b/site/index.html
@@ -134,6 +134,7 @@ <h3>One combination</h3>
 
     <footer class="page-footer">
       <p>Version <a id="build-link" href="https://github.com/ExaDev/combinatrix/releases">releases</a></p>
+      <p id="offline-status" role="status"></p>
     </footer>
   </body>
 </html>
diff --git a/site/src/pwa.ts b/site/src/pwa.ts
index f695be7..527fda1 100644
--- a/site/src/pwa.ts
+++ b/site/src/pwa.ts
@@ -18,6 +18,7 @@ function startUpdates(): void {
   const prompt = byId("update-prompt", HTMLElement);
   const update = byId("update-now", HTMLButtonElement);
   const dismiss = byId("update-later", HTMLButtonElement);
+  const offlineStatus = byId("offline-status", HTMLElement);
 
   watchForUpdates(
     // Relative to the page, so it is found under the repository's project-page path and under a preview of the build.
@@ -29,6 +30,9 @@ function startUpdates(): void {
       hide: () => {
         prompt.hidden = true;
       },
+      offlineReady: () => {
+        offlineStatus.textContent = "Ready to work offline.";
+      },
       onUpdate: (listener) => {
         update.addEventListener("click", listener);
       },
diff --git a/site/src/updates.ts b/site/src/updates.ts
index 88f5632..a05b6fa 100644
--- a/site/src/updates.ts
+++ b/site/src/updates.ts
@@ -4,6 +4,8 @@ import { Workbox } from "workbox-window";
 export interface UpdateSource {
   /** Registers the worker. Rejects when the browser cannot. */
   readonly register: () => Promise<void>;
+  /** Calls the listener when the first worker for this browser has installed and cached the site, so it will open with no network from now on. A later worker does not call it. */
+  readonly onFirstInstall: (listener: () => void) => void;
   /** Calls the listener when a newer worker has installed and is waiting for the page to let it take over. */
   readonly onWaiting: (listener: () => void) => void;
   /** Calls the listener when a newer worker has taken over the page. */
@@ -18,6 +20,8 @@ export interface UpdateSource {
 export interface UpdateView {
   readonly show: () => void;
   readonly hide: () => void;
+  /** Tells the user the site is cached and will open with no network. */
+  readonly offlineReady: () => void;
   /** Calls the listener when the user asks to update now. */
   readonly onUpdate: (listener: () => void) => void;
   /** Calls the listener when the user puts the update off. */
@@ -41,6 +45,7 @@ export interface UpdateEnvironment {
 export function watchForUpdates(source: UpdateSource, view: UpdateView, environment: UpdateEnvironment): void {
   let updating = false;
 
+  source.onFirstInstall(view.offlineReady);
   source.onWaiting(view.show);
   source.onControlling(() => {
     // A worker can also take over a page that never asked, such as the first one to install; only the update the user chose reloads it.
@@ -66,6 +71,11 @@ export function workboxSource(url: string): UpdateSource {
     register: async () => {
       await workbox.register();
     },
+    onFirstInstall: (listener) => {
+      workbox.addEventListener("installed", (event) => {
+        if (event.isUpdate !== true) listener();
+      });
+    },
     onWaiting: (listener) => {
       workbox.addEventListener("waiting", listener);
     },
diff --git a/site/src/updates.unit.test.ts b/site/src/updates.unit.test.ts
index adb719c..b301d92 100644
--- a/site/src/updates.unit.test.ts
+++ b/site/src/updates.unit.test.ts
@@ -17,8 +17,8 @@ async function outcome(failure: Error | undefined): Promise<void> {
 
 /** The worker, the prompt and the page around the update logic, driven by hand: each records what the logic asks of it and exposes the events a browser or a user would cause. */
 function setup(failures: { readonly register?: Error; readonly check?: Error } = {}) {
-  const listeners = { waiting: [] as Listener[], controlling: [] as Listener[], update: [] as Listener[], dismiss: [] as Listener[], visible: [] as Listener[] };
-  const seen = { registrations: 0, checks: 0, activations: 0, reloads: 0, shown: false, reported: [] as unknown[] };
+  const listeners = { firstInstall: [] as Listener[], waiting: [] as Listener[], controlling: [] as Listener[], update: [] as Listener[], dismiss: [] as Listener[], visible: [] as Listener[] };
+  const seen = { offlineReady: 0, registrations: 0, checks: 0, activations: 0, reloads: 0, shown: false, reported: [] as unknown[] };
 
   watchForUpdates(
     {
@@ -26,6 +26,9 @@ function setup(failures: { readonly register?: Error; readonly check?: Error } =
         seen.registrations += 1;
         await outcome(failures.register);
       },
+      onFirstInstall: (listener) => {
+        listeners.firstInstall.push(listener);
+      },
       onWaiting: (listener) => {
         listeners.waiting.push(listener);
       },
@@ -47,6 +50,9 @@ function setup(failures: { readonly register?: Error; readonly check?: Error } =
       hide: () => {
         seen.shown = false;
       },
+      offlineReady: () => {
+        seen.offlineReady += 1;
+      },
       onUpdate: (listener) => {
         listeners.update.push(listener);
       },
@@ -69,6 +75,9 @@ function setup(failures: { readonly register?: Error; readonly check?: Error } =
 
   return {
     seen,
+    installFirst: () => {
+      fire(listeners.firstInstall);
+    },
     installWaiting: () => {
       fire(listeners.waiting);
     },
@@ -101,6 +110,14 @@ describe("watchForUpdates", () => {
     expect(seen.shown).toBe(false);
   });
 
+  it("tells the user the site is ready to work offline when the first worker has installed, and offers no update", () => {
+    const { seen, installFirst } = setup();
+    installFirst();
+
+    expect(seen.offlineReady).toBe(1);
+    expect(seen.shown).toBe(false);
+  });
+
   it("offers the update when a newer worker is waiting, without activating it", () => {
     const { seen, installWaiting } = setup();
     installWaiting();