Hi @mlb92,
Welcome to the Auth0 Community!
Yes, it is possible to configure a username and password authentication for your Connection.
To do so, please enable the Requires Username toggle in your Connection settings:
(Reference: Adding Username for Database Connections)
Let me add that users can sign in with either a username or email address with their passwords. But during sign up, they must provide all three, the username, email address, and password.
I hope this helps!
Please let me know if you have any questions.
Thanks,
Rueben