As long as they don't need to be logged into multiple gmail accounts at the same time, you should be fine using Firebase Authentication. This is the normal workflow for most Google products; you select the account at sign in time.
If you are attempting to create some sort of aggregate that allows them to be logged into multiple accounts all at the same time, that's going to be problematic with existing resources. Although you might be able to call the
OAuth sign in workflow yourself and manage the OAuth tokens manually. That's well beyond the scope of what Firebase can help you accomplish.
☼, Kato