The systems that come to mind are blades in the dark (as you mentioned), and numerna (with the town expansion, I think its "building tomorrow").
Regardless of system you choose I think you will need a lot of homebrew. So I would suggest picking a lighter system if you can so that homebrew is easy/trivial. But I'm not sure what feel of game you are going for.
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?
He's mostly played Cyberpunk RED and 5e. I think his brain would melt if he had to read the GURPS rules. It is a very, very complicated system with a lot of modifiers to keep track of.
Hah, I'm an unabashed GURPS fanboy; I'm very familiar with the huge variety of modifiers! I actually find it less complicated than 5e, though - sure, there's a lot of options for modifiers; but if you need a modifier you don't know, you just eyeball it and narrate it. Look it up later if you want to check your work; but toss out anything you don't need.
There's an often-missed table describing Task Difficulty Modifiers in the core books (discussed more here: https://gurps.fandom.com/wiki/Task_Difficulty_Modifier) - this is the core of how I run GURPS. I figure out how hard I want a given task to be based on what's been described, narrate the situation, and give them a combined modifier based on what feels right. Climbing over a broken wall? Roll your Climbing skill. At night? Eh, roll at -2. We said it was drizzling earlier? Shift to -4. They're taking their time to go carefully, and risking discovery? Back to -2, and we'll roll to see if anyone comes along while they're climbing. Are those the exact right modifiers? I'unno, you want to crack open the books now, or find out what happens?
But, just to keep from overwhelming a new GM, I'd point them at GURPS Lite first - it should be able to handle most of Frostpunk okay, it's only 30ish pages, and it's free!
I haven't played it yet, but I heard that Year Zero Engine is a good system for settings when resources are scarce, running out and managing them is important
Not exactly frostpunk because it misses the whole steampunk setting, but forbidden lands expansion : the bitter reach is all about hardcore survival in a frozen wasteland and does include settlement building rules as well. It might be worth looking into though it'll need a lot of homebrew to make it exactly like frostpunk
Are you looking for a somewhat generic system that can handle a Frostpunk genre game? If so, Cypher System, Savage Worlds, Cortex Prime, or Fate would work depending on your other preferences in a system style.
I was trying to recall a TTRPG that I saw a while back that specifically focused on building a community that would work, but I'll have to post it later when I figure it out. Stupid faulty human memory.
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.