Aside from consciousness, you can understand those processes by studying the respective fields. It's true for non-experts that don't have the foundational knowledge.
I believe the argument is not that any part of those fields is incognoscible - "too complex for a human brain to grasp", but instead that the whole field is massive - "the amount of assertions and relationships required to understand the whole process is bigger than what the human brain can hold". That it is a problem of quantity, not quality; that even experts will need to abstract away and statistical average many details on these fields.
They're incognoscible in the sense that our models are very complicated metaphors, and that meta-modelling process runs out of steam at some level which we don't understand.
It's philosophical Dunning-Kruger. We don't know what we don't know. Our models are patchwork associations that have some experiential consistency, and appear "logical" based on our subjective experience of what logic is.
But that's all they are. There is no automatic implication they're complete, or even that it's possible for them to be complete.
We usually assume that limitation doesn't exist. But that seems very naive and optimistic.
