Actually, according to Paul, it seems there was already a Christian Church in Antioch even before Paul arrived:
So Paul left Peter in Jerusalem and went to Syria (where Antioch was), where there were already “churches of Judea that are in Christ” but Paul was known only by reputation.
Paul later says,
This English text implies that Paul was already there when Peter came (otherwise the normal use would be, “When I went to Antioch, I opposed Cephas to his face.”) I may be getting more context from the English text than was originally implied. But, besides that, the chronology of the Epistle recounts Paul’s arrival before it recounts Peter’s arrival.
Furthermore, the reason Paul confronted Peter was:
So Paul went to Antioch, where there was already a Christian community, then Peter joined them. But, then, James sent some Jews who subscribed to the idea that gentiles had to be circumcised (this was the first real dispute among Christians). So the church at Antioch apparently had many Gentiles and not many Jews (before the delegation from James showed up). This further suggests that Paul was active there before Peter, since Paul preached to the Gentiles and Peter preached to the Jews.
If Peter established the Church at Antioch, and Galatians is correct, then Peter must have established it very early on and returned to Jerusalem (before Paul arrived there). If other historical accounts are correct, Peter later returned to Antioch and served as its Bishop.