The theology of the Prophets before the exile had no place for the priestly blood sacrifice system. There was no atonement. The law of forgiveness worked directly and without any ritual. If Abraham, Moses, David, etc. were saved without sacrifice, it is hard to understand how blood sacrifice became necessary for salvation from the times of Ezra? How did this become necessary?
It is hard to know how to respond to this question, because it is based on an assumption which is controverted by the facts. Apparently, you read someone who claimed that the priestly system of sacrifices began post-Ezra. This is simply false. Whoever said this was making this up. We know absolutely for sure that they were making blood sacrifices in Israel at least from the time the temple was built in about 940 BC. That was the purpose of the temple, with its altar of sacrifice in the courtyard. Also, there was a tabernacle at Shiloh before the temple was built. What does the author you read propose was being done at this tabernacle? Will anyone propose that the Jews did not perform ritual sacrifices at this tabernacle? I have actually been at the site of the altar at Dan, which was used for sacrifices during the time of the Northern Kingdom. The altar at Dan has channels for carrying away the blood from the sacrifice. Isaiah talks about the sacrificial system in about 720 BC (Isaiah 1:11 and many more). This statement that the prophets before the exile had no place for blood sacrifice is simply false. What kind of scholar would make such an obviously false statement?
Now, it is true that Abraham was considered righteous because of his faith, but the covenant of circumcision and the promise was completed by ritual animal sacrifice (Genesis 15:17-21). You say that before Ezra, “the law of forgiveness worked directly and without any ritual.” What is your evidence for this statement? Where are the documents, for example in the Old Testament, that described this “forgiveness without any kind of ritual?” David made a sacrifice of a thousand bulls, a thousand rams and a thousand male lambs when he announced his son Solomon, who would build the temple (whose purpose was to offer blood sacrifice) (1 Chronicles 29:21). Unless someone wants to propose that 1 Chronicles was a complete fiction, pushed off on Jewish people who would know something about their own history, this proves that David offered many animal sacrifices. Is there any evidence of a time in the history of Israel that they did not make animal sacrifice? What is the evidence for a ritual-free Jewish religion before Ezra? What document or archaeological find supports this? I am sure that there is none.
Let me add one more thing. According to Revelation Jesus is a lamb slain from the foundation of the world. In other words, the New Testament tells us that anyone who is saved is saved by the sacrifice of Jesus, even if that salvation occurred before Jesus was born as a human being. Yes, ritual sacrifice has been part of Israel’s worship since the time of Moses and even before. There is no evidence to controvert this. But the blood of Jesus has, from God’s perspective, been the basis of atonement from the time that humans in the image of God have been on this earth.
Does this response make sense to you?