Seems to me that using computers since your childhood is not necessary, but there is something which is necessary, and which is likely to be expressed in childhood as an interest in computer programming. And, as you mentioned, in the absence of computers, this something is likely to be expressed as an interest in mathematics or physics.

So the correct model is not "early programming causes great programmers", but rather "X causes great programmers, and X causes early programming; therefore early programming correlates with great programmers".

Starting early with programming is not strictly necessary... but these days when computers are almost everywhere and they are relatively cheap, not expressing any interest in programming during one's childhood is an evidence this person is probably not meant to be a good programmer. (The only question is how strong this evidence is.)

Comparing with language acquisition is wrong... unless the comparison is true for mathematics. (Is there a research on this?) Again, the model "you need programming acquisition as a child" would be wrong, but the model "you need math acquisition as a child, and without this you later will not grok programming" might be correct.