Leviticus 16:10 But the goat on which the lot for the scapegoat fell shall be presented alive before the LORD, to make atonement upon it, to send it into the wilderness as the scapegoat. Leviticus 16:21-22 Then Aaron shall lay both of his hands on the head of the live goat, and confess over it all the iniquities of the sons of Israel and all their transgressions in regard to all their sins; and he shall lay them on the head of the goat and send it away into the wilderness by the hand of a man who stands in readiness. The goat shall bear on itself all their iniquities to a solitary land; and he shall release the goat in the wilderness.
What is peculiar about the above ritual is that the atonement is carried out after the goat of sin offering is sacrificed to God. The atonement goat is alive for carrying the sins away. How is this possible on the cross, if the sins were placed on the Messiah before His sacrificial death?
I'm not versed enough in OT ceremonies, so I don't know for sure if order is even important, but ponder these passages:
John 1:29 The next day John seeth Jesus coming unto him, and saith,
Behold the Lamb of God, which taketh away the sin of the world.
<-- atonement for sin
John 1:30 This is he of whom I said, After me cometh a man which is preferred before me: for he was before me.
John 1:31 And I knew him not: but that he should be made manifest to Israel, therefore am I come baptizing with water.
John 1:32 And John bare record, saying, I saw the Spirit descending from heaven like a dove, and it abode upon him.
John 1:33 And I knew him not: but he that sent me to baptize with water, the same said unto me, Upon whom thou shalt see the Spirit descending, and remaining on him, the same is he which baptizeth with the Holy Ghost.
John 1:34 And I saw, and bare record that this is the Son of God.
(Same event; different Gospel Book)
Matthew 3:13 Then cometh Jesus from Galilee to Jordan unto John, to be baptized of him.
Matthew 3:14 But John forbad him, saying, I have need to be baptized of thee, and comest thou to me?
Matthew 3:15 And Jesus answering said unto him, Suffer it to be so now: for thus it becometh us to fulfil all righteousness. Then he suffered him.
Matthew 3:16 And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him:
Matthew 3:17 And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.
Matthew 4:1
Then was Jesus led up of the Spirit into the wilderness to be tempted of the devil.
Matthew 4:2 And when he had fasted forty days and forty nights, he was afterward an hungered.
So there we have sin laid upon Jesus, then led into the wilderness and then later on in His life He is the actual sacrificial Lamb. Not sure if gender was the key but the "with a blemish" sure was. He was both the Scapegoat AND the sacrificial Lamb of God.
There is another passage that may be as useful in understanding this; the passage about Jesus and Barabbas. Matthew 27:14-26.