I have an app where the default option is to store user data as a local SQLite database, however, I want to add the option if the user wants to sign in and tran
Firebase's real-time database is indeed one of the best solutions for your problem. It has a generous free plan and is well integrated into Android Studio. And if your data structure is simple enough, you can drop SQLite altogether and use Firebase's offline storage. This will allow Firebase to automatically handle syncing of offline data for you(syncing is usually painful to implement by yourself).
Alternatively, you could build your own web app and expose a REST API to your android application. This gives you the advantage of having control over everything. I would however not recommend this because of the amount of knowledge and time required.