Bubble backend - flutter app integration

We have a bubble website that we want to connect with an existing flutter app. We have done the Implementation and Social platforms configuration (google auth) within the Flutter app, but the problem is how do we connect the user login auth with google to the backend workflow in bubble for the user?

The steps we follow to do the google auth are listed below:

1- Creating a project in the firebase console.

2- Registering the android &iOS app and download the files and put them in the android & iOS project folder.

3- Filling the A.App info in firebase (OAuth consent form) B.App domain.

4- Package Name :

Default Activity Class Name :

5- key hash.

you can do a bubble-firebase connection via zapier. Better to visit zapier’s documentation for this.