You can initialize your library project configurations manually as below,
For more info, kindly refer working-with-multiple-firebase-projects-in-an-android-app
Also go-through how-does-firebase-initialize-on-android to understand; how the Firebase module is getting initialized by itself.
For Android apps using Firebase, there is a central FirebaseApp object
that manages the configuration for all the Firebase APIs. This is
initialized automatically by a content provider when your app is
launched, and you typically never need to interact with it. However,
when you want to access multiple projects from a single app, you'll
need a distinct FirebaseApp to reference each one individually. It's
up to you to initialize the instances other than the default that
Firebase creates for you.
FirebaseOptions options = new FirebaseOptions.Builder()
.setApplicationId("1:530266078999:android:481c4ecf3253701e") // Required for Analytics.
.setApiKey("AIzaSyBRxOyIj5dJkKgAVPXRLYFkdZwh2Xxq51k") // Required for Auth.
.setDatabaseUrl("https://project-1765055333176374514.firebaseio.com/") // Required for RTDB.
.build();
FirebaseApp.initializeApp(this /* Context */, options, "secondary");
Hope I've answered your question.