firebase-authentication-dotnet | C # library for Firebase Authentication | Authentication library

Background on my login flow:

I'm creating a C# WPF Application which will be distributed to an end-user.

On my Website, I'm using FirebaseUI Auth to do the login authentication so that the user can log in with Google, Facebook or Email.

When the user initiates a log into the Application, it transfers the user over to the Website temporarily which mints a custom JWT token on the server which is returned to the Website then -> Application and then Application then uses to the freshly minted JWT token to Authenticate with FirebaseAuthentication.net to generate a Firebase auth token. This works great for connecting to Firebase REST API's like Firestore to obtain user information on client Application.

The Problem: Not only do I want to connect to the Firebase API's, but to the Google Cloud Speech API as well (in this case Speech-To-Text). I don't believe the Firebase auth token is sufficient to achieve this. I can verify the user and access their Firebase data on the server or the client, yet this is insufficient to connect to the Google Speech-To-Text API. In Google's examples using the client credentials first requires obtaining an auth-code from their authorization endpoint. In Google's Windows Application OAuth Example This is the https://accounts.google.com/o/oauth2/v2/auth authorization endpoint.

Theorizing creates another potential question which could sooner answer the question: Could I use my FirebaseUI Auth page as an OAuth Endpoint to somehow authenticate my End-User Application with Google to connect to the Google Speech-to-Text API instead of using the https://accounts.google.com/o/oauth2/v2/auth endpoint?

The Question: How do I access the Google Cloud Speech-To-Text API from an end-user Application after authenticating them with Firebase Auth?

Google's reference for how to authenticate as an end-user: https://cloud.google.com/docs/authentication/end-user