I don't think Google treats a web app hosted on firebase any differently than a web app hosted anywhere else; Google automatically indexes everything it can find. Officially, Google finds websites by looking for links and sitemaps. So, if your staging environnement is not linked to anywhere and you don't submit a sitemap directly to Google, in theory you shouldn't get indexed.
But, I wouldn't just count on the fact that you're not putting links out there. Links might find themselves online for some reason at some point in the future.
You could add a robots.txt to your staging site with this value:
User-agent: *
Disallow: /
But in my experience, an even better solution is to make your staging site unaccessible without a username/password. That way, Google's bot won't be able to index anything else than a login form. And if people do find your staging URL, they won't be able to see what's going on there.
Most people actually try hard to be indexed very high and it's not that simple. Since your goal is to NOT rank high, should be very easy. It's like trying to not win a game.