Nope. Here is that verse -Hebrews 9:22.
In fact, the law requires that nearly everything be cleansed with blood, and without the shedding of blood there is no forgiveness.
Without the shedding of blood there is no forgiveness.
The shedding of blood is necessary (it is a sacrifice, or more precisely a korbanot, which literally means "to draw near"). This was not to appease God's. This was NOT the atonement.
Since the shedding of blood was necessary, but not the actual atonement (not making atonement for sins), what was the actual atonement?
The priest made atonement for the people (and before this for himself) by taking blood to the alter and applying that blood.
See -
He shall then slaughter the goat for the sin offering for the people and take its blood behind the curtain and do with it as he did with the bull’s blood: He shall sprinkle it on the atonement cover and in front of it. In this way he will make atonement for the Most Holy Place because of the uncleanness and rebellion of the Israelites, whatever their sins have been. He is to do the same for the tent of meeting, which is among them in the midst of their uncleanness.
and is to splash some of the blood of the sin offering against the side of the altar; the rest of the blood must be drained out at the base of the altar. It is a sin offering.
The life is in the blood.
Same with Passover. It was necessary to offer a lamb. That lambs blood had to be shed.
BUT the killing of the lamb, the shedding of blood, was not what delivered them from death. It was the blood applied to their door posts.
You have misunderstood the significance of the OT sacrifices. The life is in the blood.