Though maybe a cheat engine could simulate a few branches of possible inputs a few steps ahead and adjust inputs when it discovers split-second advantages?
But there are bigger exploits. IIRC, the client sends separate actions for buying a unit/tech/building and paying resources, and the other clients don't enforce that they go together. This allows malicious clients to buy without paying. It's been seen a few times even in the ranked mode of the Definitive Edition remake. https://www.reddit.com/r/aoe2/comments/fjjudp/cheaters_are_a...
This way of doing things made sense for the time, and the execution was impressive. It was pretty reliable, nobody wanted to cheat anyway, and yes lag was a big problem but there wasn't another good way to do it back then. Nowadays they should have something else IMO.
Finally found a genuine use for the blockchain, since the server is only used for the lobby!
Mine virtual AoE gold and record it in the distributed ledger. Primitive path finding is also AI, so now you just need some investors!
The only exploits that are inherently applicable in the case of a simultaneous deterministic simulation model are those of the information-revealing class (e.g, "maphack"). This is where a standard AH system comes in.
The obvious one is that the client knows where everything is on the map, even when hidden by fog-of-war - so client-side hacks can reveal that.
A hacked client can easily desync the game too, or stall it and cause it to time out if the player is losing.