Jeremiah 31:31-34
31 “Behold, the days are coming, declares the Lord, when I will make a new covenant with the house of Israel and the house of Judah, 32 not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt, my covenant that they broke, though I was their husband, declares the Lord. 33 For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people. 34 And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the Lord,’ for they shall all know me, from the least of them to the greatest, declares the Lord. For I will forgive their iniquity, and I will remember their sin no more.”
It helps tremendously to not impose English connotations on the original language and try to read the English meaning into the text, rather we are to try to read the original language with its own connotations and how it was intended to be used, and this can be understood in the English perfectly fine despite the language barrier.
The Hebrew word אזכר means to bring to remembrance. To call to mind. It’s a deliberate act of the will. This is not referring to the ability to memorize. The information being memorized is inferred and assumed, or if the information was written, it is inferred and assumed that it is available for recollection and accessible for retrieval, meaning it is not lost. It’s to bring attention to, to prioritize, or to focus upon.
The Greek in the NT uses μνησθω and the LXX uses μνησθω, the same word. It means to remind. It too is a deliberate act of the will.
If God says, He will remember no more, it means that He is choosing by a deliberate act of the will to refrain from recalling or reminding Himself about something.
This is not the same as saying God forgets. Rather this is God saying, that He has made a decision to avoid reminding, recalling, or drawing upon a piece of information, that is in His possession, but which He refuses to call upon. In a sense, He is distancing Himself from the information so that He does not look upon it.
The impossibility of recalling this information lies in God’s character, not in the availability or lack of availability of the information, the moment He says He won’t do something, we can be assured that He won’t do it, because it’s impossible for God to lie
Hebrews 6:18
in which it is impossible for God to lie,
This is a self-imposition that God puts upon Himself. The knowledge and information are not impossible to retrieve, as though God had deleted, lost, or forgotten it, rather He refuses to access it and His refusal makes it therefore by inference and by extension an impossibility for God to recall or remind Himself of those sins.
In Conclusion
No God hasn’t forgotten the sins, He just chooses to never recall, remind or if you prefer, He chooses to never remember those sins literally, forever. It’s a self-imposition and based on His character we can be assured, not only that He won’t mention them, but that He won’t access them for Himself either. It is His deliberate choice to limit His knowledge or awareness of said deeds.