Well, Acts 12 says Herod Agrippa died before the Antioch laying on of hands. Josephus reports he died in A. D. 44. Paul's first missionary journey began between 46-47 A.D. Paul was in Arabia for three years after his conversion and then spent one year at Antioch. Galatians 2 says he went up to Jerusalem after 14 years.
It is impossible for for your scenario to have taken place. Paul was sent out by the church at Antioch before his visit to Jerusalem mentioned in Galatians 2.
“Uh, did you forget Antioch, which Peter DEFINITELY founded??”
Acts 11:19-26, “Now they which were scattered abroad upon the persecution that arose about Stephen travelled as far as Phenice, and Cyprus, and Antioch, preaching the word to none but unto the Jews only. And some of them were men of Cyprus and Cyrene, which, when they were come to Antioch, spake unto the Grecians, preaching the Lord Jesus.
21 And the hand of the Lord was with them: and a great number believed, and turned unto the Lord. Then tidings of these things came unto the ears of the church which was in Jerusalem: and they sent forth Barnabas, that he should go as far as Antioch. Who, when he came, and had seen the grace of God, was glad, and exhorted them all, that with purpose of heart they would cleave unto the Lord.
For he was a good man, and full of the Holy Ghost and of faith: and much people was added unto the Lord. Then departed Barnabas to Tarsus, for to seek Saul: And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.”
I see the persecuted “men of Cyprus and Cyrene”, and Barnabas and Saul, but I don't see Peter mentioned. Where do you find Peter founding the church at Antioch?
History. The FACT of Peter founding the Church of Antioch is well-documented in the historical record, including records from the first century AD. But, as I said, because "...it's not in the Bible...", you'll simply blow off the evidence (which, to me, is rampant intellectual dishonesty).
There are other sources of truth than the Bible, buddy.