See the autocomplete attribute.

Set it to current-password or new-password as applicable.

Based on chromium; this should work : (the suggest password comes after already known passwords for that site)

<form id="login" action="signup.php" method="post">
  <input type="text" autocomplete="username">
  <input type="password" autocomplete="new-password">
  <input type="password" autocomplete="new-password">
  <input type="submit" value="Sign Up!">
</form>

more examples : https://www.chromium.org/developers/design-documents/form-styles-that-chromium-understands

"Suggest strong password" is available on Chrome for Android as explained here:

When you want to generate a secure password:

1. Turn on sync in Chrome.
2. Go to a website and sign up for an account.
3. Tap on the password text box.
4. Tap Suggest strong password.
   • If you don't see this option, tap Password Save your password and then Suggest strong password.
5. You'll see a preview of the password. To confirm, tap Use password.
6. Finish signing up for your account. Your password is automatically saved to Chrome.

However, there is an issue with newer versions of Chrome that does not allow the suggestion to appear as testified here or here by many. As suggested on those links, removing the Chrome updates allows the suggestion message to appear.

On the left, when I uninstalled Chrome updates, on the right Chrome's latest version

Suggested pasword on old version

You can also try to change your autofill service as suggested on one of the posted links.

Or you just wait for future versions to fix the issue.