God did inaugurate the OT sacrificial system. But you are not talking about the Hebrew religion. You are speaking about the pagan ANE practices from which God called His people (transferring sins to animals, appeasing God's by animal sacrifices, etc).
No, the doctrine of transfer of sins and animal sacrifices is talking about the old covenant being the fore runner of the New covenant. It taught the righteousness of Christ and his kingdom when spiritually discerned. The spiritual seedline/remnant saw this and could therefore prophesy of the New covenant, by the spirit of Christ in them. Luke 3:23-38.
The old covenant was righteous in its context and purpose.
2 Cor 3:7. But if the ministration of death, written and engraved in stones was GLORIOUS, so that the children of Israel could not steadfastly behold the face of Moses for the glory of his countenance, which glory was to be done away with.
3:8 How shall not the ministration of the spirit be rather glorious?
3:9. For if the ministration of condemnation be glory, much more doth the ministration of righteousness exceed in glory.
3:10 For even that which is made glorious had no glory in this respect, by reason of the glory that excelleth.
3:11 For if that which is done away with (transferring sins to animals, appeasing God by animal sacrifices that represented in types and shadows the righteous work of Christ) WAS GLORIOUS much more that which remaineth is glorious.
When David sinned and brought the wrath of God upon Israel, he bought Ornan's threshing floor, built and altar and offered burnt offerings and peace offerings and called upon the name of the Lord. This appeased the wrath of God. Who do you think the burnt offerings and peace offering represented?
It was the perverting of what the sacrifices meant, by the influence of the nations, that the Lord was calling Israel out from.
The old covenant has been fulfulled and done away with. What is meant has not been.