Without a hint of shame or embarrassment or any sort of profound internal conflict, Jesus openly admits he is--or at least was, while living under the conditions of the fall and fulfilling all righteousness for us--ignorant of at least one thing: "concerning the day and hour [of my return] no one knows, not even the angels in heaven, nor the Son, but the Father alone" (Matt 24:36 || Mk 13:32).
Though it may not have created any difficulties for Christ, this passage is notorious in theological discussions of the incarnation. Predictably, some argue it's evidence Jesus was not divine. That, of course, is impossible to square with the rest of Scripture. Others, with Peter-like zeal, deny he ever said such a thing--hence the footnote on Matt 24:36 in your ESV, that "some manuscripts omit nor the Son." But that's a favor too far, and one that robs us of the wonder of the cross just as Peter would have done when he rebuked Jesus for announcing he was going to be crucified (Matt 16:22).
God insists we contemplate the scandal of the incarnation: the eternal Son had to become fully human; he had to be the anti-Adam and empty himself, take on the form of a servant, and obey all the way to being crucified. There's no way around the scandal and offense of these things, and there's no way around the fact that the omniscient and eternal Word endured ignorance for us and our salvation.
Just how he was able to endure ignorance is not entirely clear to us (more than one possible explanation is on the orthodox table). But he did and this is no small matter. Consider Calvin's comment on Matt 24:36 || Mk 13:32:
The chief part of our wisdom lies in confining ourselves soberly within the limits of God's word. That men may not feel uneasy at not knowing that day, Christ represents angels as their associates in this matter; for it would be a proof of excessive pride and wicked covetousness, to desire that we who creep on the earth should know more than is permitted to the angels in heaven. . . . And surely that man must be singularly mad, who would hesitate to submit to the ignorance which even the Son of God himself did not hesitate to endure on our account.
To say that the omniscient Son endured ignorance on our account is in no way "an insult offered to the Son of God," he argues. On the contrary, it shows how great his grace is toward us in how far he has gone in self-denial to save us from our sin:
For we know that in Christ the two natures were united into one person in such a manner that each retained its own properties; and more especially the Divine nature was in a state of repose, and did not at all exert itself, whenever it was necessary that the human nature should act separately, according to what was peculiar to itself, in discharging the office of Mediator. There would be no impropriety, therefore, in saying that Christ, who knew all things, (John 21:17) was ignorant of something in respect of his perception as a man; for otherwise he could not have been liable to grief and anxiety, and could not have been like us, (Heb 2:17).
the objection urged by some--that ignorance cannot apply to Christ, because it is the punishment of sin -- is beyond measure ridiculous. For, first, it is prodigious folly to assert that the ignorance which is ascribed to angels proceeds from sin; but they discover themselves to be equally foolish on another ground, by not perceiving that Christ clothed himself with our flesh, for the purpose of enduring the punishment due to our sins. And if Christ, as man, did not know the last day, that does not any more derogate from his Divine nature than to have been mortal.
To be clear, Calvin does not argue that the Son ceased to be divine or omniscient in the incarnation, only that he denied himself, for the purpose of accomplishing our redemption, the benefit or use of his omniscience. It was a voluntary act of self-denial in which the divine nature "did not at all exert itself." In other words, Jesus lived among us, while fulfilling all righteousness for us, just as one of us--and this is a glorious thing.