With a large number of DNA sequences, the genetic cause can be separated from environmental. That's why embryo selection is possible.
Getting parent's DNAs sequenced might be needed but it's affordable now. See gwern's answers and link for more info.
Yes, it can be inferred: https://en.wikipedia.org/wiki/Heritability_of_IQ.
Can it really be inferred? Not including conditions or syndromes of course. The parents' environment may have affected their intelligence and the child may turn out entirely different.