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God shows Peter in a vision that he can eat anything, clean and unclean, then sends him to the house of a Gentile, Cornelius, who is filled with the Holy Spirit. Peter and the believers in Jerusalem (all Jews) accept this means God accepts Jews and Gentiles; Barnabas takes Saul to Antioch about the same time: Acts 10–11

It was about a decade after Jesus’ death and resurrection that believers were first called Christians, presumably from Paul’s emphasis in his preaching of Christ crucified:

Acts 11:25-26 Then Barnabas went on to Tarsus to look for Saul. When he found him, he brought him back to Antioch. Both of them stayed there with the church for a full year, teaching large crowds of people. (It was at Antioch that the believers were first called Christians.)

This is believed to have been around 40AD.

See: Timeline from Apostle Paul’s Birth to his First Missionary Journey