I can't specifically help you on that library you are using, but have you looked at this? https://developers.google.com/accounts/docs/OAuth2Login
If you do an authorization for login as well, you'll get a token back and you can use that to get the userid of the user at Google
This field is only present if the https://www.googleapis.com/auth/userinfo.profile scope was present in the request for the access token. The value of this field is an immutable identifier for the logged-in user. Store this and you should have a durable identifier of the user.