The short answer to your question is, unfortunately, no, Losant cannot have the Firebase SDK implemented directly for user auth. Mostly because authentication of Experiences happens within a Workflow.
However, there is an alternative, since you are already using the Firebase DB as a means of maintaining user credentials there is a workaround I would suggest investigating. Firebase provides a RESTful API (https://firebase.google.com/docs/reference/rest/auth), and Losant can leverage its HTTP nodes in an Experience Workflow to authenticate the user’s credentials.
The process here would not be a direct SSO type experience but rather, the user can login to your experience page, and the email/password credentials would be sent to the Firebase API using the HTTP node (https://docs.losant.com/workflows/outputs/http/), and the workflow would then need to validate the response from the Firebase API and allow the user to login.
We recently released a guide on configuring SSO within Experiences using Active Directory, it’s a great example of using a custom authentication scheme along with Experience Users (https://docs.losant.com/guides/how-to-configure-single-sign-on-within-experiences-using-active-directory)