Cobwebster please open a new discussion if your request is different from the existing topic... In particular when it's 3 years old.
As far as I know there's no Firebase login extension at this moment, but there's no doubt one could be made.
If you are interested in developing it yourself, check if Firebase has oauth available, and whether there's an existing PHP League driver for it. If there's a driver, it's as simple as what the Facebook and GitHub extensions do. If no driver exists, you can create it fairly easily.@
If it has some very strange system (non-oauth), it's still possible. You could take a look at the Flagrow Telegram extension for an example of an odd login API.