I cannot answer the OP Poll question because my answer would be both.
Now, I realize that sounds like an impossibility, but there are many scriptures that seem to say God knows everything from the beginning (which I believe), and there are many verses that seem to say God knows some things in time (which I also believe).
I have a theory on this, and that is that God does limit himself at times in dealing with men. God has to limit himself in dealing with men because if he appeared in his glory men would fall dead on the spot.
Jesus must have limited himself to appear in the presence of men. And perhaps this is why he did not know the exact day and hour of his return, but only his Father.
Well, what about the many times God appeared to men in the OT, such as when he spoke to Adam and Eve, Cain, Abraham and many others? Perhaps at these times he had to limit himself in order to appear in presence with men, else the men would be killed by his presence.
If this were true, it would explain why God asked Adam and Eve where they were in the garden, why he asked Cain where Abel was, why he said he would personally go into Sodom to see if they were doing according to the cry he had heard and then he would know, or telling Abraham that NOW he knows Abraham fears God.
So, perhaps when God comes down from heaven and appears to men in person he has to limit himself in some fashion.
We know Jesus is God, but the scriptures say no man hath seen God at any time.
John 1:18 No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him.
This seems like a contradiction, because the scriptures say God appeared to men many times.
Gen 33:And the LORD spake unto Moses face to face, as a man speaketh unto his friend. And he turned again into the camp: but his servant Joshua, the son of Nun, a young man, departed not out of the tabernacle.
Gen 35:7 And he built there an altar, and called the place Elbethel: because there God appeared unto him, when he fled from the face of his brother.
8 But Deborah Rebekah's nurse died, and she was buried beneath Bethel under an oak: and the name of it was called Allonbachuth.
9 And God appeared unto Jacob again, when he came out of Padanaram, and blessed him.
Gen 17:1 And when Abram was ninety years old and nine, the LORD appeared to Abram, and said unto him, I am the Almighty God; walk before me, and be thou perfect.
So, John 1:18 says no man has seen God at any time, and yet we have several instances where the scriptures say God appeared to men. How can these both be true?
I think if we understand that God MUST limit himself to appear before men (because men would die), then we can understand this seeming contradiction. God did appear to Jacob and Abraham, but not fully, not in his glory. So, in this sense no man has truly seen God at any time.
And if God limits himself in glory, perhaps he also limits himself in other attributes including omniscience. This would explain why Jesus did not know the day and hour of his return, and why God at times seemed only to know things in time such as Gen 18:21 and Gen 22:12.
Gen 18:21 I will go down now, and see whether they have done altogether according to the cry of it, which is come unto me; and if not, I will know.
Gen 22:12 And he said, Lay not thine hand upon the lad, neither do thou any thing unto him: for now I know that thou fearest God, seeing thou hast not withheld thy son, thine only son from me.
God cannot appear in glory before man or he will die.
Exo 33:17 And the LORD said unto Moses, I will do this thing also that thou hast spoken: for thou hast found grace in my sight, and I know thee by name.
18 And he said, I beseech thee, shew me thy glory.
19 And he said, I will make all my goodness pass before thee, and I will proclaim the name of the LORD before thee; and will be gracious to whom I will be gracious, and will shew mercy on whom I will shew mercy.
20 And he said, Thou canst not see my face: for there shall no man see me, and live.
21 And the LORD said, Behold, there is a place by me, and thou shalt stand upon a rock:
22 And it shall come to pass, while my glory passeth by, that I will put thee in a clift of the rock, and will cover thee with my hand while I pass by:
23 And I will take away mine hand, and thou shalt see my back parts: but my face shall not be seen.
So, we see before the scriptures said Moses spoke to God face to face. But this was not God in his glory or full attributes. Later when Moses asked to see God's glory, God told Moses he could not see his face or he would die.
This is what I believe. I believe that God limited himself at times dealing with men in person. In these instances he surely did not appear in his glory, but he may have also been limited in other attributes such as omniscience.
I do not know for absolute certain this is correct, but it could be.