The Body of Christ actually started when the old covenant ended.
Luke 16:16
The law and the prophets were until John the baptist:
Since that time the kingdom of God is preached, and every man presseth into it.
The New Covenant is the house of Jesus, He is the High Priest over the New Covenant which get started in earnest with the arrival of John the baptist who was the the forerunner of Jesus
Hebrews 3:5,6
And Moses verily was faithful in all his house, as a servant, for a testimony of those things which were to be spoken after; But Christ as a Son over His own house; whose house are we, IF we hold fast the confidence and the rejoicing of the hope firm unto the end.
Now, there is a new house, the Body of Jesus Christ! Under the New Covenant that the Lord said would come forth, we see Jesus Christ as the High Priest. The old covenant with it’s laws and regulations have been taken away because thru Jesus Christ a new and better covenant has come in to place.
Hebrews 10:9
Then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second.
(God said He would make a New Covenant - see Jeremiah 31:31-34)
Hebrews 8:6
But now hath Jesus obtained a more excellent ministry, by how much also Jesus is the mediator of a better covenant, which was established upon better promises.
And with the changing of the priesthood, God’s Word tells us there is also a change of the law.
Hebrews 7:12
For the priesthood being changed, there is made of necessity a change also of the law.
And sadly some who start of getting born again becoming member of the Body of Christ end up falling away departing from the faith and quit abiding in Christ.