I would recommend looking hard into
Firebase for this project, especially if you do not have dedicated full-stack or backend members on your team.
The real time database, as you mentioned, is a great option, but I would also look into
Firestore. Similar to RTDB, it adds more functions and some cool methods as well. Also, another great thing about Firebase is you have easy access to storage and dead simple auth as well.
Apollo are great technologies as well, and may be the better option if you do not wish to cede as much control to third parties in your application.
Overall, I say if you wish to focus more time developing your
React application instead of other parts of your stack,
Firebase is a great way to do that.