I have never used GURPS, but if its post-apocalyptical, you could have a city builder system where you have to worry about food and water. Maybe you have to go into ruins to find old technology to research and upgrade your stuff kenshi style.

I have found that some players enjoy avoid combat at all cost, while other enjoy finding every opportunity to jump into it. The best you can do is provide tools to deal with it. Like dnd has a lot of abilities related to combat because that’s what they want you to focus on. You can try to find some rpgs that have don’t have a combat focused for inspiration. Edge of the empire has the colonist class that is not focused on combat. Although I have never played them, I hear that games of thrones rpg and star trek adventures has focuses on that don’t rely on violence. Also Comrades: A Revolutionary RPG might be worth checking out.

I guess a bigger question is what type of game to you want it to be? It could be a spy romp where you are counter intelligence against some fascist/capitalist nation. It could be a survival focused where you try to solve issues that face the society that is try to survive in an uncaring world. Could be a bit of both or something different. That should guide your conflict and how it appears in your world, as well as the tools the players have to resolve them.