You answered your own question, even if you don't like the answer. If God said eating brown M&Ms atoned for sin, then that's what it would be. He's God. He makes the rules.
There is somewhat more to it, though. Sin offerings were primarily for unintentional sin, not deliberate sin. Offerings were also made for thanksgiving and other things. You may look at the sin offering as a symbol of the offeror's repentance. The offering itself was not efficacious in removing sin. Without repentance, the offering was worthless.
There are also many other methods than animal sacrifice described as atoning for sin. Later writings emphasized repentance and prayer. And that is how, in the absence of the Temple, Jews go to God for forgiveness.
WHY and HOW do you think killing a God-man makes someone's shoplifting charge go away in the eyes of God?
Belief in the impossible involves truly giving oneself to God as Lord of one's life. That was the point with Abraham. That is the point with the death, burial, and resurrection of Christ.
Sheep, however, don't have names....they are bought merchandise. They get killed to be eaten all the time.