Here is one theory about the origin of the Coptic Church. I’m no specialist and I can’t claim to pass judgment on it one way or the other. I’m just repeating something I found in a reputable source, Arnold Toynbee (ed.), The Crucible of Christianity.
The Coptic Church may have derived from Judaeo-Chrstian missions, although its origins remain obscure. Certainly Paul never reached Egypt, and the presence in Africa of large Jewish communities suggests that the earliest missionary activity there may have been Judaeo-Christian.
You mention Luke and Mark at the end of your post. Luke was one of Paul’s aides, secretaries, and fixers, while Mark is thought to have acted in a similar capacity for Peter.