Is it possible to make a creature larger than the standard 2x2? For example, 3x3? I'm not having much luck. Or rather, it seems to work, considering that the model doesn't occupy the entire space, but that's not a big problem. The real issue is that if you place such a creature on an adventure map, the battle with it doesn't start. What should I do? Or is it still impossible?

Exactly as Jass said. But! There are some nuances. For example, if you put one 3x3 creature and one 1x1 creature in a squad, the battle starts normally, and the creature will stand in its place. I don't know how it works, but it's been tested.
Other problems are possible. For example, if you summon squads to a random position during a battle, they may be summoned onto a creature that has been enlarged, and the entire group will get stuck. Accordingly, in such cases, you need to control it.