Yes but it can be both innate and built on statistical models, contrary to Chomksy.

The idea that there is some level of statistical inference involved in language acquisition is not contrary to generative thought, look at Charles Yang's work or Lidz or a fair number of other people. Chomsky just thinks this is uninteresting so he is dismissive of it.

The central question remains whether there are categorical rules built into the brain for grammar (plus "some" statistical inference possibly), or whether the entirety of our grammatical processing is statistical. It is entirely possible that evolution encoded statistical priors into our brains with grammar overall being a fully statistical process. Therefore, the fact that children learn more quickly isn't really hard evidence one way or another.

[delayed]

Well, Chomsky wouldn’t be happy, that’s the point of OP; he explicitly argues against this.

But the statistics only work well at vastly unrealistic scales of data, and the learning pattern doesn't match children's behaviour at all.

A statistical model is approximating the brain at some level.