There was a great experiment with chimps and human babies that shows a critical difference in our thought patterns. Researchers put grapes in a cage and gave the chimp/child a rake with tines wider than the grapes. They showed the chimp/child how to use the rake tines to slowly, laboriously scrape the grapes into reach. Both the chimp and child were able to quickly copy what they were showed.
Here is the difference. The child immediately realized that they could flip the rake over and use the flat part to drag all the grapes over in one quick swoop. The chimp never made that logical jump and kept copying the slow way it was shown.
The ability to rapidly envision other options and innovate is a distinct difference from apes/monkeys and humans. This isn't determined by any one gene. It's a complex combination of multiple genes. It is significantly harder to breed for something like this than for example brown hair or green eyes. Not impossible, but unlikely.