The law is made to restrain us and punish us if we go past its lines. Unfortunately all sin requires blood. This is why I often am confused at jewish people who pray for forgiveness. They don't have a messiah (Jesus) who is their sacrifice yet they live their lives without sacrifice. It's the same as living lawless in my eyes.
The Law was made neither to restrain nor to punish us but to show us what we have done. What restrains us is our Freewill if we make good use of it and what punishes us are the "magistrates" or the consequences of our transgressions as in the law of cause & effect.
It is not simply praying for forgiveness that forgiveness comes. We must set things right with HaShem so that our sins, from scarlet red become as white as snow through repentance and return to the obedience of God's Law. (Isaiah 1:18,19)
We spent 70 years in Babylon without a Temple and sacrifices; at the end of that time, our sins that had caused that exile had been expiated without a single sacrifice. (Dan. 9:24) it means that sacrifices never had the role to forgive sins. Sacrifices were added by Moses only to make the exodus easier to happen. The truth of the matter is that HaShem never commanded that sacrifices be part of the religion of Israel. (Jeremiah 7:22)
Last but not least, Jesus could have never been a sacrifice for our sins because he knew that it would be against the Prophets of the Most High to die for the sins of another. (Ezekiel 12:3,20)
