When did God begin His plan of redemption?

The plan of redemption began immediately after Adam and Eve sinned and God lost them. At that moment He set in motion the purchase of the whole human race through the seed of the woman, revealed in Genesis 3:15. Though centuries passed before it became reality, its beginning was right after their sin.

Les teaches that redemption means paying a price for something that was once yours and you lost it. That is exactly what happened to the human race: it was God's in Adam and Eve, but He lost it when they sinned. As soon as He realized He had lost it, as shown in Genesis 3:15, He immediately kicked in gear a plan of redemption through the seed of the woman. It took centuries before it became a reality, but it all began right after Adam and Eve sinned. He put in motion the plan of buying back the whole human race, which is what Paul is teaching in Romans 3. There, redemption is freely by His grace, and God set forth the Lord Jesus to be a propitiation through faith in His blood.

Genesis 3:15

And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.

Where does the promised line of redemption begin and how far does it run?

The promised line of redemption begins at Genesis 3:15, where the seed of the woman would crush the head of the servant, and it runs all the way through Scripture as the scarlet thread of salvation. It is the continuous promise of redemption.