Hello Pearl, that is an interesting thought, one that I've never heard before (specifically "when" Jesus became sin for us .. 2 Corinthians 5:21).
The thing that we need to be very careful of, I think, especially when we wade out into the deeper waters concerning Deity, is not allowing our thoughts to move us into the realm of heresy (this reminds me a bit of a discussion that I had some years ago about the Father being the "Fountain" or "Source" of the Godhead, because how can Beings, specifically God the Son and God the Holy Spirit, who have no beginning, have a source?)
So, while it's true that He carried our sins/became sin for us (something which I suppose He could have done from the foundation of the world if He chose to?), never, not even for a split second, did He actually become a "sinner" personally. So, since there was never a point in time when He was not perfectly innocent and perfectly righteous, personally, how could there be a time, then, when He was unable to forgive sin 
Also, I believe that it was His death, not His dying, that made/makes atonement for our sins, although He did say, just prior to yielding up His spirit, “ELI, ELI, LAMA SABACHTHANI?” that is, “MY GOD, MY GOD, WHY HAVE YOU FORSAKEN ME?” (Matthew 27:46)
This is all very interesting, and there is much to consider, so thank you for that 
God bless you!!
--Papa Smurf
2 Corinthians 5
21 He made Him who knew no sin to be sin on our behalf, so that we might become the righteousness of God in Him.
Becoming sin for us is not something we can comprehend. Imagine taking on trillions of sins for all time ... and knowing them), one has to be omniscient to do that. There is that kind of spiritual eternal knowledge that we can't fathom. We can barely comprehend the totality of our own sins.
I have been told that the Father turned away from Him, that the Father could not look upon sin. At what point did this happen? Likely when He was arrested in Gethsemane, from that time to death. He was shuffled back and forth from the Sanhedrin, to Pilate, then Herod, and back to Pilate and the mob, then the scourging, the walk to Calvary, being nailed to the cross, to death, He was not incommunicado with the Father. So it was only naturally human to respond, in his exhaustion, pain and suffering, "Why have you forsaken me?" He was also quoting Psalm 22.
Nevertheless, He still asked the Father to "forgive them for they know not what they do".
Not all of them! No, not all are saved.
His purpose, to die for our sins, was a Priestly act of intercession. In the peak of His pain and suffering on the cross with all the mocking, He interceded with a prayer to the Father for the world ( Isaiah 53:22), that they might be saved - if they believe.
This is the meaning of the Cross summed up, FORGIVENESS, that the world would be offered forgiveness, salvation.if only they would seek God and ask.
For God did not send his Son into the world to condemn the world, but that the world might be saved through him.
John 3:17
He was on a mission of mercy. Forgive them Father for they know not what they do. They are ignorant. But were the Sanhedrin ignorant? They did not know He was God in the flesh. No, they accused Him of blasphemy, putting Himslef equal to God, and claiming to be able to forgive sin. But did Jesus forgive all? No, I don't think so. He condemned the Pharisees: You brood of vipers... white-washed tombs ... who will save you from the Gehenna? Still the prayer went out to all. How was it answered? Immediately with the criminal next to him, then the centurion changed his mind, then Pentecost came and forgiveness began to flow throughout the world.
Acts 6:7 says many of the priests who condemned him changed their minds and put their faith in him. So it was that Jesus asked the Father to not hold His murder against them, for some will soon know what they did and change their minds and hearts... but not everyone.
