Knowledge cannot be passed on via your DNA to our descendants (obviously), so any innate knowledge about the world found in our brains must have been found through natural evolution. But...
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2) as brains change, so does the world; evolutionary scales (# of trials required by evolution as a search process) are too long to stumble upon adequate knowledge for the current state of world, so such knowledge would have to be limited to long-term invariants (which are few)
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3) there just isn't a lot of storage space in the part of your DNA that's related to your brain; it's a few megabytes, so you couldn't store much in terms of pre-trained connectome
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A pre-trained connectome developed by evolution is how insects work, but not humans; that approach is extremely behavior-centric and pretty limited in what sort of knowledge it can produce. The innate part of human cognition is mostly about how to learn -- not knowledge itself.
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That does not follow. Genome codes a complex developmental program composed of powerful interacting modules (proteins, microRNAs, ...) that in turn assembles the body including the brain.
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However efficient the compression mechanism being used, and even taking into account the interaction with information that's external to our DNA, it remains that a pre-trained connectome would have a certain entropy, and that our DNA has limited entropic capacity.
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That’s enough for very important information.
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I think is wrong to simply link information quantity to a logic gates number. Information is entropy. It is superficial to measure entropy without a reference system. It's like you would say: the signal have 6 dB. dB what ? dBU, dBm
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