Intelligence has been evolving and subject to inheritance far longer than that.
Believe it or not, the scenario you describe has occurred to researchers as an avenue of study, and they found it didn't amount to much(i.e. nature over nurture), see 'twin studies.'
This subject, intelligence, is really one of the triumphs of 20th century science, in that it has come to be quite well understood. It's understandable that you and so many others seem unaware of this, however, because to quote Steven Pinker, 'people hate the message.' https://twitter.com/sapinker/status/645301814955388930
Also, you may consider abandoning this notion of genetics and culture being in an uncorrelated relationship.
Cultures are simply people, that is they are emergent from the interactions of people, and since there are high IQ people and low IQ people, there are high IQ cultures and low IQ cultures.
On this note I have found that replacing g/IQ with height in any conversation about human genetics make for a more civilised discussion.
It would work like this: My parents were poor, and had lower IQs. They didn't have time to read to me or talk a lot to me or spend a lot of time with me. They were too tired, just trying to make enough money to keep us all fed.
Now I've got kids, and I'm repeating the same pattern, partly because I'm tired from working too hard, and partly because that's the pattern I saw growing up, and so it's the default behavior for me.
Note well: This account is fictional, not my actual experience. It's not even anecdotal evidence for my position. It's a hypothetical explanation of how cultural baggage could be inherited between generations in a way that could affect IQ.