I wrote a long reply earlier and accidentally erased it. Now I see there are some good suggestions!
Now I’ve been to anxious to play this game so I watch others play it. I had a bunch of absurd ideas. Some I have used at some point in other games.
Make the absolute sorriest character you can. The worst stats you can muster all together and survive that way.
Role play. Choose a few restrictions for that character. Like maybe your character refuses to drive a car anywhere after the “incident,” for example.
Or maybe they’re a pacifist and refuse to kill any zombies at all. That sounds awful actually.
Decide to collect one random item and make it a goal. Ex., to have the worlds biggest bleach collection.
I’ve walled off whole neighborhoods and created a town in other games. You could do that and play Zombie Sims.