In the Bible book of Proverbs, a wise man is one who is patient, and "it is to his glory to overlook an offence" (transgression, or sin, against him). Proverbs 19:11. However, the Bible is clear that God never 'overlooks' sin, for all sin is known to him, and is judged by him, but if it is truly repented of, God forgives and calls that sin no more to his remembrance (Isaiah 43:25 & 65:17). God's patience is involved, and he does give time for people to repent.
Yet, on the other hand, he is seen in Old Testament times to sometimes immediately strike down others. He judges thoughts, intentions of the heart, and knows all the circumstances involved. A great deal depends on what the particular sin is.
Take, as an example, the sin of Shimei in 2 Samuel chapter 16. He cursed king David who was fleeing from his son, Absalom, also pelting David and his entourage with stones. Shimei claimed God was giving the kingdom to Absalom. When Abishai sought David's permission to kill Shimei, David refused, trusting in God to be repaid with good for the cursing he was receiving that day. When Absalom died and David returned in triumph to Jerusalem, Shimei appeared again, grovelling this time (2 Samuel 19:18-23). Once more, Abishai wanted to kill Shimei, but David again refused. He promised Shimei that he would not kill him. But, before he died, he charged Solomon with remembering the sin of Shimei, that it would not go unpunished (1 Kings 2:8-9) for Shimei had not repented of his sin.
"And remember you have with you Shimei son of Gera, the Benjamanite
from Behurim, who called down bitter curses on me the day I went to
Mahanaim. When he came down to meet me at the Jordan, I swore to him
by the Lord, 'I will not put you to death by the sword.' But now, do
not consider him innocent. You are a man of wisdom; you will know
what to do to him. Bring his grey head down to the grave in blood.' 1
Kings 2:8-9 N.I.V., 1987 ed. [Bold mine]
Solomon gave Shimei time, making a covenant with him, to stay in Jerusalem, but 'the day you leave and cross the Kidron Valley, you can be sure you will die; your blood will be upon your own head." vss. 36-37
Three years later, Shimei broke that covenant by chasing after some servants who had run away, bringing them back. Solomon was told, and confronted him with the fact that he had broken his oath to the Lord. "Now the Lord will repay you for your wrongdoing" vs. 44. Shimei was give plenty of time to repent. But he seemed to think getting his servants back was more important than getting God's forgiveness for cursing the Lord's anointed, and so he broke his covenant with God.
So, there is a biblical example of God allowing plenty of time for an individual to repent, but if they think lightly of their sin, and that they "have got off with it", they will discover God has not overlooked, far less forgotten their sin, no matter what time elapses. Repentance brings total forgiveness, and their sins no more being remembered by God (Psalm 103:12). Refusing to repent, no matter how much time is allowed, brings God's judgment. Such unrepented-of-sin is never overlooked by God.
As for when this concept took root, I would suggest Joseph freely forgiving his brothers (in Genesis, from chapter 37 to 45) is a very early lesson the Israelites would begin to grasp.