Thank you for your question.
It is possible to automatically redirect users straight into the Google auth flow when they land on the wp-login.php page. If they have already authenticated, and are logged in to exactly one Google account in the browser, they will go straight through the auth process and into the site.
To try this out (plus some other tricks around this process) take a look at the Advanced Options docs:
https://wp-glogin.com/docs/google-apps-login/configuration/advanced-options/
If you are building an intranet for example, these options could allow you to do what you describe – your intranet plugin will redirect to wp-login.php if the user (logged out of WordPress) tries to access a page, the plugin can redirect straight to Google, and then Google redirects straight back and the user should land on their intended page, logged in.
It really depends on how your site is set up in other ways.
If you would like to discuss in more detail, let me know more about your site in an email: [email protected]
Regards,
Dan