There is nothing built into Firebase Authentication to allow only users you've invited to sign up. When the email+password provider is enabled, anyone can call the API and register.

What you can do though is have a list of the invited email addresses in an online database somewhere (such as Firebase's Realtime Database of Firestore) and check against that list whether a user is authorized after they have signed in.

For an example of how to limit access to the database to specific users, have a look at:

• for Realtime Database: How do I lock down Firebase Database to any user from a specific (email) domain?
• for Firestore: Restrict Firestore gmail sign in to specific domain