Please check out screens/GoogleLoginScreen.js.
The only change is replacing the result variable. The relevant docs can be found here. Scroll to the bottom.
I did this test for a group project. We ended up not going forward with it. While the app does seem to authenticate with Google, we never figured out what we needed to do next. If you figure something out, I'd love to hear it! Otherwise, I just want to warn you this repo might be false hope.