Please how can I make the google sign up/sign in authentication flow to show my custom domain added on the app instead of the primary default url provided by the app?
Go to App Hosting within your Firebase Console. Create a backend which will appear in Google Cloud Run within your Google Cloud Platform environment.
Within App Hosting select the Settings tab and choose Domains.
Follow the steps display under Domains to connect your app to a custom domain.
Once connected and once your app is published, you’ll be able to see your site live at the domain you enter.
The “Sign in with Google” site you see in the image is controlled by the Credentials within your API & Services tab in your Google Cloud Platform environment.
That has been done but its the same thing.