Doing finish the initial level cheev could be challenging because some areas REALLY have a lot of enemies - notably the prison - where it's very easy to get xp and level up. Not to mention that you can't level up at the initial game where you're stocking up some abilities. In order to get Card, it'll take 40 AP, in order to get Card Mod it'll take 100 ap iirc. Going to have to find a good way to also get W-MG Refine early without leveling up too. Fuck yes.

You would have to run away from all enemies in the fire cave and the world map, and beat Ifrit for some 20 AP towards the 40. You theoretically beat the Fastitocalon-F for the extra 20 but you'd be killing them in the process but you're looking at 6-13 xp per kill, with a cap of 1000 xp required to level. So definitely possible.
I'm already thinking on how to do this run.
FFVIII

I've done a lot of low level runs, I've never done a Don't Level Up run.

And unlike those losers who use Enc-None or Enc-Half, I just card every enemy because I like the challenge.

Here are my rules for this run:
- No leveling up, ever.
- No running away except at the beginning.
- No Enc-None or Enc-Half except in that dungeon where you fight Ultima Weapon because FUCK THAT PLACE.
- Card. Every. Enemy.

If it's a human, turn them into stone.