It's nice to throw around claims like that, or like "microtubules connect the brain the quantum realm" (Penrose). Fortunately that's not how science works.
It is not. There are many biological examples of random processes generating patterns and weights, such tiger stripes, fingerprints, etc. DNA only encodes the reaction, but the pattern itself is seeded by initial position of random molecules, not the DNA.
> that it influences the initial state of the brain.
You've gone from "DNA is probably the seed for the random initialization", as in the deterministic seed for a PRNG, to "influences". Those are 2 different claims.
Most scientists will agree that DNA encodes the large-scale connectivity in the brain, ie from region to region, thickness of corpus callosum etc.
Most scientists will disagree that it is "probable" that DNA encodes/seeds the weights of each and every synapse.
My own reading of the poster's intent aligns with this: "DNA encodes the large-scale connectivity in the brain, ie from region to region, thickness of corpus callosum etc."
Most biologists will fully disagree with the whole premise, and support the reverse claim that we are born with random weights, we learn to walk/speak English/etc after we're born. Not from weights seeded from our DNA.
At least Penrose had the good manners to make relevant contributions (meaning Chomsky effectively managed to steer his field in entirely the wrong direction, take everybody along with nothing to show for it. Nobody uses his contributions today in study. Yes he's celebrated ... but why? He's like a prime minister that presided over a country causing an economic crisis, throwing everyone into misery. I guess those are exactly the kind of politicians celebrated. Bush is celebrated while he destroyed half the economy, Clinton is forgotten (well, except for that one thing) despite being the best president of the last 50+ years economically)