I\'ve setup firebase_auth and google_signin about 6 times, but in my latest app I must have forgotten a step.
firebase_auth: ^0.11.1 google_sign_in: ^4.0.1+3
I set the support e-mail address and the LOGO in Google :
e-mail
LOGO
Google
Developers Console > API and service > Credential > Oauth Consent Screen.
After this set up all is working.