As someone answered Firebase hosting does not include mails. You have different services: authentication, database, storage, hosting, functions, test lab, crash reportinf, etc.. but no emails.
Here is my suggestion:
* You should have a standard hosting service that provides everything including space for your web, mails, ftp services, and much more. Including DNS services that you can use to redirect something
* Then you redirect your http services to Firebase. This could be your entire domain or a subdomain. Using the Firebase console and following the instructions
That's all you need. But I could also recommend a great solution for your email. You can use "Google for Works" that includes emails, 30 Gb Google Drive space per user, and much more. The cost is USD5/month/user. (Just one user is not a problem). And it also supports domain redirection so you follows a similar procedure as before for using your own domain.
So your main hosting basically redirect to whichever service you have for each of the components of an internet solution.
This is what I made and it's working fantastic. Good luck.