We are put into the body of Christ by the gospel of the grace of God that was given to Paul the Apostle by the Lord Jesus Christ.
Ephesians 3:6 KJV
That the Gentiles should be fellowheirs, and OF THE SAME BODY, and partakers of his promise in Christ BY THE GOSPEL:
Acts 20:24 KJV
But none of these things move me, neither count I my life dear unto myself, so that I might finish my course with joy, and the ministry, which I have received of the Lord Jesus, to testify the gospel of the grace of God.
The gospel of the grace of God is not found in Acts 1-13. The substitutionary death, burial, and resurrection is not preached yet.
The gospel of the grace of God was not being preached until it was given to Paul.
Galatians 1:11-12 KJV
But I certify you, brethren, that the gospel which was preached of me is not after man.  For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.
Paul had to be the one to communicate that gospel to the rest of the disciples, which proves they were not preaching it yet.
Galatians 2:1-2 KJV
Then fourteen years after I went up again to Jerusalem with Barnabas, and took Titus with me also.  And I went up by revelation, and communicated unto them that gospel which I preach among the Gentiles, but privately to them which were of reputation, lest by any means I should run, or had run, in vain.
If the other Apostles already knew the gospel of the grace of God, they would not have any controversy and dispute in the Jerusalem Council over salvation (Acts 15). That proves the majority of believers in general (who were taught by the twelve) were not in the body until Acts 15.
I had always thought the body started in Acts 2, but what happened in Acts 2 with the Spirit poured out on Pentecost was prophesied of. The body of Christ is a mystery hid in God and not made known until Paul.
Acts 2:15-16 KJV
For these are not drunken, as ye suppose, seeing it is but the third hour of the day.  But this is that which was spoken by the prophet Joel;
Ephesians 3:1-6,9-10 KJV
For this cause I Paul, the prisoner of Jesus Christ for you Gentiles,  If ye have heard of the dispensation of the grace of God which is given me to you-ward:  How that by revelation he made known unto me the mystery; (as I wrote afore in few words,  Whereby, when ye read, ye may understand my knowledge in the mystery of Christ)  Which in other ages was not made known unto the sons of men, as it is now revealed unto his holy apostles and prophets by the Spirit;  That the Gentiles should be fellowheirs, and of the same body, and partakers of his promise in Christ by the gospel:  And to make all men see what is the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ:  To the intent that now unto the principalities and powers in heavenly places might be known by the church the manifold wisdom of God,
I do not believe the Church started in Acts 9 either because the gospel of the kingdom is still being preached. Jesus did not give Paul the gospel of the grace of God on the road, He didn't give him any gospel. Jesus told Paul to go talk to Ananias, who baptized Paul so he could receive the Holy Ghost. Ananias was preaching the gospel of the kingdom, not the gospel of the grace of God. The gospel of the kingdom requires water baptism for salvation (Mark 16:15-16).
Acts 9:17-18 KJV
And Ananias went his way, and entered into the house; and putting his hands on him said, Brother Saul, the Lord, even Jesus, that appeared unto thee in the way as thou camest, hath sent me, that thou mightest receive thy sight, and be filled with the Holy Ghost.  And immediately there fell from his eyes as it had been scales: and he received sight forthwith, and arose, and was baptized.
Acts 22:12-16 KJV
And one Ananias, a devout man according to the law, having a good report of all the Jews which dwelt there,  Came unto me, and stood, and said unto me, Brother Saul, receive thy sight. And the same hour I looked up upon him.  And he said, The God of our fathers hath chosen thee, that thou shouldest know his will, and see that Just One, and shouldest hear the voice of his mouth.  For thou shalt be his witness unto all men of what thou hast seen and heard.  And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord.
Paul wasn't in the body until after Acts 13 because in Acts 13 Paul still is the subject of prophecy, not of mystery, as God commanded him and Barnabas to preach to the Gentiles from Isaiah's prophecy:
Acts 13:46-47 KJV
Then Paul and Barnabas waxed bold, and said, It was necessary that the word of God should first have been spoken to you: but seeing ye put it from you, and judge yourselves unworthy of everlasting life, lo, we turn to the Gentiles.  For so hath the Lord commanded us, saying, I have set thee to be a light of the Gentiles, that thou shouldest be for salvation unto the ends of the earth.
Isaiah 49:6 KJV
And he said, It is a light thing that thou shouldest be my servant to raise up the tribes of Jacob, and to restore the preserved of Israel: I will also give thee for a light to the Gentiles, that thou mayest be my salvation unto the end of the earth.
The Body began when the word of the Lord's GRACE was testified of in Acts 14:3.
Acts 14:3 KJV
Long time therefore abode they speaking boldly in THE LORD, WHICH GAVE TESTIMONY UNTO THE WORD OF HIS GRACE, and granted signs and wonders to be done by their hands.
The solution to the doctrinal problems in the Gospels and General Epistles is that the Gospels and James were written before Acts 12, before Paul shared with the Jerusalem church the truth of Christ's blood atonement, and the rest of the General Epistles and Revelation were written between Acts 12 and 15 when they knew the blood atonement, but didn't yet know the Pauline mysteries of the body of Christ.
The proof that Paul wrote the last of the Bible is this:
Colossians 1:25 KJV
Whereof I am made a minister, according to the dispensation of God which is given to me for you, TO FULFIL THE WORD OF GOD;
The word "fulfil" breaks down into full fill, to fill full. Paul filled full the word of God by completing the canon of scripture. There are no General Epistles or Gospels or Revelation written after Paul. The last book of the Bible, historically, is 2 Timothy, meaning that Paul was really talking about ALL scripture (not just the Old Testament) when he wrote this:
2 Timothy 3:16-17 KJV
All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:  That the man of God may be perfect, throughly furnished unto all good works.
Paul also was talking about ALL the Bible and dividing the doctrine in the Gospels and Epistles when he wrote this:
2 Timothy 2:15 KJV
Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth.
Did the Body start at the Cross? No. Notice in the next verse that the word is "by," not "at." The cross made the body of Christ possible, but this is not when the body began.
Ephesians 2:16 KJV
And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:
Weren't there people in Christ before Paul?
Romans 16:7 KJV
Salute Andronicus and Junia, my kinsmen, and my fellowprisoners, who are of note among the apostles, who also were in Christ before me.
The people in John 15 were in Christ as branches in a vine that could be cut off and burned in hell. They were not part of the Body of Christ. Jesus hadn't even died yet. There are also saints in the Lord in Revelation 14:13 in the Tribulation.
John 15:1-7 KJV
I am the true vine, and my Father is the husbandman.  Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit.  Now ye are clean through the word which I have spoken unto you.  Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.  I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.  If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned.  If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you.
The church of God does not have to mean the body. There have been churches of God since the Old Testament.
Galatians 1:13 KJV
For ye have heard of my conversation in time past in the Jews' religion, how that beyond measure I persecuted the church of God, and wasted it:
Acts 7:38 KJV
This is he, that was in the church in the wilderness with the angel which spake to him in the mount Sina, and with our fathers: who received the lively oracles to give unto us:
There was a church of God even before Jesus died.
Matthew 18:17 KJV
And if he shall neglect to hear them, tell it unto the church: but if he neglect to hear the church, let him be unto thee as an heathen man and a publican.
I do not believe this should be a subject that we break fellowship over. There are so many different views on when the body of Christ started, but to me, this makes more sense Dispensationally. Many will say this is a "Hyper" view, but so is believing in Dispensational salvations. I am not going to ignore scripture because I might get labeled a Hyper Dispensationalist. According to Ephesians 3:6, we are put into the body by Paul's gospel, so the body could not have started before Paul's gospel was revealed.