Hi,
If you don’t use Social Login then you can keep it in test mode, since the production mode is required only if you want to allow third-party users (not the app admins) to authenticate via the Google OAuth window.
Please try it with a third-party Google account (e.g. ask a friend to sign up or if you have another GMail account which is not set as the OAuth app admin), if I remember correctly the test mode allows only admins for testing purposes, but to collect third-party account profile details and emails (required for creating an account via Social Login) switching to production is required.