I’m only marginally familiar with Frostpunk as a genre - what sort of game is your friend looking for? Gritty apocalyptic survival with some settlement building aspects?

Ironsworn could be easily tweaked to fill that need, I think. I suspect Savage Worlds could too. I see a lot of suggestions at https://forum.rpg.net/index.php?threads/frostpunk-tabletop-system-recommendations.858901/ too.

If I may ask, why is GURPS not desirable? I know it has a few supplements for exactly this; including character templates to simplify chargen.

Can you elaborate on what frostpunk means and what you want out of a frostpunk rpg?

It really depends what kind of game you want to play.

If you want a fiction first game where the characters are a bunch of “freedom fighters” in an hostile environment, you could try either Spire or a|state, but you would need to heavily modify the settings. It would be a lot easier with a|state, which is a dystopian future hack of blades in the dark.

Maybe a modified twilight 2000 or Mutant Year Zero? It depends on how grim or heroic he wants the game to be.

My guess is he wants a steampunk setting with survival and base building mechanics.