Firebase's free tier is more than enough to play with an idea, and the next tier up is (100k concurrent users) $25/month ... if that's too expensive then there's something very wrong with your pricing model. Obviously this assumes you're not storing much data per user - you wouldn't build a imgur clone with it - but it's not that expensive for any typical SaaS app.
Concurrent users are not the only limitation. Your app needs to fit the bandwith limits as well. I had to shutdown a very simple app with a few users because of ridiculous billing.
