If you want a relational database for just one user's data, you could read a SQLite data file over the network when your user opens the app, perform SQL queries over the data in memory, then write the entire database file back across the network when the user hits a "save" button.
But you probably don't want a "save" button, you just want the user's state to be constantly updating back to the server.
And you probably don't want to write back the entire data file every time you save, just the parts that have changed.
So Firebase is optimized to solve these problems, and I bet the data structures they use are not also optimized for supporting all kinds of relational queries.
If you want a relational DB as a cloud service, it sounds like you want Cloud SQL (as far as GCP is concerned).
(Disclaimer: I work on GCP.)
(Fellow GCPer.)