Before you can integrate Google Sign-In into your website, you are required to have the Web client ID and Web client secret. For that, you must create a Google Firebase Console project.
Follow these steps to integrate the Google sign-in to your store:
Google Firebase re-signs your app with a new key on publishing. You must update your mobile app with the new signing key for the Google Login to work on your published.
Following are the steps
Go to your app settings on Firebase and add the SHA Fingerprint key.
You should be able to use Google Login on your published app now.