Sorry, I missed the bit about google in your original post. You can’t create a social user with an upstream IdP (i.e. google). You need that user’s permission and need to have them log in via the google login prompt to have the profile added to Auth0.
Now, it’s possible to avoid the Auth0 prompt and direct them straight to the IdP by passing a connection param with the request to authorize. This may give you the desired login experience.
Then, if you want to access the user’s google tokens to interact with the API, you can get them in the user’s profile from the auth0 management API, here.