I'm pretty new to firebase hosting and wanted to know if the static websites hosted using firebase will show up in search results with the domain name provided by Firebase. For example the website hosted as 'abc.firebaseapp.com' or 'abc.web.app' will show in the search results after getting a good number of hits or should I go for a custom domain?
Yes they will show up in search results. There is not much difference than other hostings you could use beside the free website URLs abc.firebaseapp.com and abc.web.app.
Your SEO has not much to do if it is hosted on Firebase or elsewhere. Just try to do your best following the Google instructions.
I would also recommend a custom domain because it would improve your overall SEO performance.