1) sell it. You’re competing with Google. Not gonna fly.
2) embed ads. You can now get Google to pay you. Sounds nice, except Google’s own browser doesn’t do that.
3) donations and grants. This could work with a government with enough foresight to ensure viable browser competition, which isn’t even a theoretical problem. Getting enough money to pay for anything but coffee and electricity may be a problem, though.
4) run an ad network and make sure your browser shows those ads ‘better’ than the competition: kinda makes sense, except you don’t need the browser here to make money? Google already makes one, after all. So you need some kind of a long term contract between the ad network and the browser development branch to make sure the browser part keeps doing the browser.