SuttaCentral
No.
In other Buddhist forums I see all sorts of questions asking what the Buddha had to say about all sorts of contemporary issues. Things that a man living over 2,600 years ago could not possibly have an opinion about. Sure enough, those opinions aren’t there.
my understanding from MN90 is that the buddha says:
There is no ascetic or brahmin who knows all and sees all simultaneously: that is not possible.
in the context of that sutta, this suggests to me that everything that is capable of being known is knowable by the buddha if he turns his mind to it.
however, there are two aspects to this: 1) some things are effectively unknowable, and 2) a buddha needs to turn their mind to the question to be known to know it. until that point they do not know it.
we get point these points from the buddha’s own words on knowing whether there is a first cause for the universe - i believe he says he looked back and back and back into his previous lives and was unable to see a first cause to the cycle of becoming. if i recall correctly, he doesn’t say there is no first cause, but just that as far as he looked back, there was none. in other words, he did not know this immediately on enlightenment - he had to turn his mind to this question (point 2 above), and this question had no answer that he could see (point 1 above).
in this sense, he is not omniscient - he doesn’t know everything at any one time. he needs to turn his mind to a given question at hand.
this resolves the question noted elsewhere in this thread of why the buddha didn’t know some monks would commit suicide - namely, he didn’t turn his mind to that question at the relevant time.
The technical way it’s defined in Abhidharma acknowledges that a person can only actively know one thing in any given moment, so it’s impossible to know everything simultaneously. They, thus, considered the common meaning of omniscience as being nonsense. I should also say that I was repeating a Sarvastivada position that I read in Chinese years ago, not a passage in the Theravada Abhidhamma.