It's almost impossible to have a proof of the genetic component because you can't have a control subject and since there are many variables that are connected to social and psychological environment of a child. And also because with eugenics there is a very strong political factor. And also because the way we determine intelligence might be biased (we know the IQ test is).

You would have to find thousands of couples across different social classes with low intelligence levels. Then you'd have to somehow get those couples to have non-identical twins one of which would be from a sperm donor with higher intelligence levels than them. Best case scenario is for the couples to not be aware of this happening so they treat both children the same way. Then you'd have to observe those kids for 20-30 years (again without them knowing) making sure the kids go though roughly the same lives, environment, and development.

If the vast majority of kids with half their genes from a higher intelligence do better than their siblings with lower intelligence genes only then you'd be able to have a more precise speculation if there is a genetic component or not.