From your other comment, you mention realtime systems. This is a different problem from a database and has more to do with communications. Firebase just packages things together for you. For example, Postgres (a relational DB) has LISTEN/NOTIFY which can allow listeners to distribute messages to connected clients. Or you can skip integrating the comms with the database altogether and just notify connected users completely from code when things happen.
It's pronounced Diane. I do data architecture, operations, and backend development. In my spare time I maintain Massive.js, a data mapper for Node.js and PostgreSQL.
From your other comment, you mention realtime systems. This is a different problem from a database and has more to do with communications. Firebase just packages things together for you. For example, Postgres (a relational DB) has LISTEN/NOTIFY which can allow listeners to distribute messages to connected clients. Or you can skip integrating the comms with the database altogether and just notify connected users completely from code when things happen.
Redis is also a possibility if your data model is pretty lightweight and the main focus is on publishing/subscribing to events.