When was the live goat brought forward in the Day of Atonement ritual?
The live goat was brought forward only after the high priest had finished the atonement ritual inside the tabernacle, completing reconciliation of the holy place and the tabernacle of the congregation. At that point, he brought the live goat, laid both hands on its head, and confessed Israel's iniquities over it.
Les explains that after the high priest had presented the blood of the goat on behalf of the children of Israel and came back out, he then moved to the scapegoat. The live goat was brought forward when he had made an end of reconciling the holy place and the tabernacle of the congregation—after he had finished all the ritual within that little tent. Then Aaron laid both hands upon the head of the live goat and confessed over it all the iniquities of the children of Israel. Les also emphasizes that even this scapegoat pictures Christ.
And when he hath made an end of reconciling the holy place, and the tabernacle of the congregation, and the altar, he shall bring the live goat: