Weldon asked: “Why does God require a blood sacrifice?
I want to begin by acknowledging that God, in His sovereign plan, determined what would be required and what would not be required for salvation. It’s unfruitful to speculate on what other possible means God could have established. God determined that for men and women to be saved, there must be the shedding of blood. I accept that as God’s plan and desire because it’s what the Bible teaches.
One verse we need to consider is found in Leviticus 17:11
For the life of the flesh is in the blood, and I have given it for you on the altar to make atonement for your souls, for it is the blood that makes atonement by the life. (ESV)
One thing to clarify is that God is connecting the shedding of blood with the giving of a life. For example, in the sacrificial system, the Israelites could not simply pick an animal, and gather a few drops of blood for the alter. That wouldn't be sufficient.
When we think of our salvation that Jesus accomplished, Jesus could not have shed a little blood on the cross and then come down off of it. He had to literally give his life. So the shedding of blood is a reference to the giving of an innocent life in exchange for the life of a guilty person.
This goes all the way back to Genesis 3 where God took the lives of animals, fashioned their skins into clothing, and gave the clothes to Adam and Eve as a covering. Those skins replaced the fig leaves that Adam and Eve had created. The leaves were man's attempt to make atonement. But God’s plan involved the shedding of blood.
The author of Hebrews makes it clear that the sacrificial system of the Old Testament is completed in Christ.
 But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation)  he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption.  For if the blood of goats and bulls, and the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh,  how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God. (Hebrews 9:11–14 ESV)
 Indeed, under the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness of sins. (Hebrews 9:22 ESV)
We have here in Hebrews the teaching that Jesus Christ ties everything together. Jesus died, once for all, shedding his blood, giving us life so that we can meet the requirements for the payment of the wrath of God through the sacrifice of an innocent life. And of course, Jesus Christ was the innocent Lamb of God who came to take away the sins of the world.
Thanks for asking, Weldon.