“Every single early Christian in the early Church was a Jew.”
Sure, as long as you aren’t counting Luke. The Colossian letter differentiates Luke from followers who are of the circumcision, indicating that Luke’s culture was gentile. And Luke’s usage of pronouns in Acts suggests that he was a native of Troas, a region of Greek cities on the west coast of what today is Turkey.
Yes correct, Luke was a Greek Doctor. He’s the exception however. I’m speaking of the early “early” Church. As the Church spread, it’s Gentile population grew as well naturally.