Oh well, that much is easily answered. The Buddha was asked about the origin of the universe, and answered that when an origin is sought, a beginning is not seen. Notice that he did not say there was no beginning, nor did he deny it. This because the concept of a beginning simply does not apply. I suggest that to an omniscient mind, the nature of the universe is evident, but it is so radically different from everything we assume about the nature of reality, that the true state of things simply cannot be jammed into our preconcieved paradigms.
So it appears the Buddha cannot answer the imponderables and thus does not know. But the appearance is false.
Does that help? It's not quite answering the exact question you asked, but it's close.
Not exactly, though I appreciate the effort.
I have read that Vasubandhu can be interpreted as stating that the Buddha's omniscience is non-empirical. If that is true then it is not possible to explain it in common terms anyway.
I had interpreted omniscience to mean that a Buddha, by perceiving the nature of all things, knows all things in their totality. Hence, by apprehending emptiness completely without obstruction, they "know everything".
However, it has been stated in this thread that this is categorically not what is meant; and what is meant is that Buddhas know all objects of knowledge, either immediately or if they choose, such as the number of hairs on an ant's leg in Africa or whatever. So not (just) knowing the nature of the Universe, but knowing all the possible variations of trivial facts about the Universe.
This seems contradictory both to the idea that Buddhas do not apprehend mental objects and also to dependent origination - to the extent that knowledge of ants and so on are not even relatively true, as ants and hairs are conceptual designations of the most base kind, they have no existence whatsoever beyond mere imputation and categorisation of a deluded perceiver. There is nothing there to know, since they are all empty.
So I am wondering how this is explained and so on. There must be a conventional explanation for it, or else it wouldn't be taught. It is taught constantly. So it is not as easy to move aside, as with questions of "when did time begin" and so on.
I consider this to be related to the topic, but perhaps it is not. Sure, it is conceptual proliferation. But perhaps to just abandon the problem that would be responding to attachment with aversion, not understanding. If all conception is proliferation, what use is a Buddhist forum? Presumably, it is to generate relative understanding, hopefully as a basis for ultimate understanding. So it has a function. If what is functional is ignored or bypassed, it becomes dysfunctional, not virtuous. But, hey-ho, I can just add it to the list of "shit I don't understand" if it comes to it. Cup of tea, anyone?