I was facing the same issue and I have used the web o auth client id and using that i haven't faced any issues and i also got back the id token from google . so you can try that .

I have used google_services.json file when I was using authentication with help of google firebase but as much I have read you don't need to use google_services.json file when you are authenticating the app with help of google cloud console .

p.s- please someone reply on this if he/she has used or enabled any api on google console and it has worked in case of authentication .