The first thing to do, no magic or skill required is verify whether it’s the generator or the AC that is the problem.
Plug it into shore power. Even a good solid 15A residential outlet with no other loads on the circuit “should” get the AC going. 20A for sure will.
Could very well be a bad genny. My few experiences with cheap generators have been hit n miss. Few years ago we bought a bunch of 2k Yamaha knockoffs at Costco for running flagger stations.
My engineer at the time tried using one to run the AC in his old camper. Tried 3 different units , all new or almost new. 2 of the 3 would overload and not start the AC. But a new actual Yami 2k and an old beat up Honda 2k worked consistently.