How to update a file that I deployed to Firebase Hosting?

You cannot change hosted files in the Firebase Console.

Instead, you should change the index.html on your local copy where you initially ran the firebase deploy command. Once you're done with the changes, run firebase deploy again to push the updated version of your website to Firebase Hosting.

For small changes it is probably faster to run firebase serve. This spins up a local web server, so that you can test the changes. Once you're satisfied they work, publish them to Firebase Hosting with firebase deploy again.

Update: this is now possible through some custom scripting. See my answer here for details: Upload single file to firebase hosting via CLI or other without deleting existing ones?