not sure not remembering, and not knowing, are the same thing.
also, omniscient God not remembering sin is an incredibly profound mystery!
Gen 9:15
And I will remember
H2142 my covenant, which
is between me and you and every living creature of all flesh; and the waters shall no more become a flood to destroy all flesh.
Gen 9:16
And the bow shall be in the cloud; and I will look upon it, that I may remember
H2142 the everlasting covenant between God and every living creature of all flesh that
is upon the earth.
Clearly, the Hebrew ZaKaR does not mean "not having something in one's awareness and being prompted to put one's mind on to that something of which one was not previously aware". God is not going to
forget that He had made a covenant between Himself and mankind, and every living thing. It seems to mean here "to act upon knowledge one has". So when God says , He will remeber our sins no more, He means He will not act upon the knowledge He has of our sins.
So, in
Gen 8:1
"And God remembered
H2142 Noah, and every living thing, and all the cattle that
was with him in the ark: and God made a wind to pass over the earth, and the waters assuaged," God acted upon His knowledge of Noah and the creatures with him on the ark.
In
Gen 19:29
"And it came to pass, when God destroyed the cities of the plain, that God remembered
H2142 Abraham, and sent Lot out of the midst of the overthrow, when he overthrew the cities in the which Lot dwelt," God acted upon the knowledge He had of Abraham and Abraham's concern for Lot.
And in
Gen 30:22
"And God remembered
H2142 Rachel, and God hearkened to her, and opened her womb," God acted upon the knowledge He had of Rachel and her prayers for a child.
I could go on to the other occurrences of ZaKaR.
In
Gen 40:14
"But think
H2142 on me when it shall be well with thee, and shew kindness, I pray thee, unto me, and make mention
H2142 of me unto Pharaoh, and bring me out of this house:" Joseph asks the butler to act upon his knowledge (Qal of ZaKaR) of Joseph and to cause Pharaoh to act upon his knowledge (Hiphil of ZaKaR) of Joseph in prison.
The usual sense of remembering is not what the Hebrew word ZaKaR means, despite it being translated as such in many Bible versions.