Has anyone tried to connect Firebase with Google groups?

Dear Members,

I’m having a big number of users on google groups, I want them to be able to login to discourse via the Google Auth Page but obviously, they must be on my group list.

While, it seems like it’s not possible to do some sort of SSO via Google Groups, I found this following option on firebase :

Has anyone tried this ? How is it working ? Is it suitable for my issue ?

Thank you all for your help !