It is important here to understand the point of Acts 13's sermon. This sermon was in a synagogue and is Paul speaking without any pressing issue or circumstance. This is the official, sample sermon.
1, the promises to Israel were actually to Christ.
Wrong. The promises to Israel were to Israel.
2, the resurrection of Christ is the proof of the 1st.
Why do you think that he was resurrected?
Even in the New Testament there is NOT ONE SINGLE WITNESS
of his resurrection. No man saw him get up from the grave and walk away.
Oh, but he appeared to his disciples. Well, in that case, can you explain to me why nobody recognized him? Look in Luke 24:13-35. This speaks about the men on the road to Emmaus. He met them, but they didn't recognize him.
The same thing happens in John 20:14; "At this, she turned around and saw Jesus standing there, but she did not realize that it was Jesus. "Woman," he said, "why are you crying? Who is it you are looking for?" Thinking he was the gardener, she said, ... "
She thought he was the gardener....
John 21:4 "Early in the morning, Jesus stood on the shore, but the disciples did not realize that it was Jesus. He called out to them, ..."
And again they didn't recognize him.
Isn't it strange that they didn't recognize the person with whom they were so close for years?
But the NT gives the answer to that strange phenomena. Look in Mark 16:12-13 "Afterward Jesus appeared IN A DIFFERENT FORM to two of them while they were walking in the country."
So it was a person "in a different form" from the previous well known person who appeared to them, that's why they didn't recognize him.
A person in different form from the old Christ, who was not recognized by the people he interacted with for years, only days before, doesn't that sounds like an impostor who is pretending to be the resurrected messiah?
That also explains why some of the disciples doubted when the "resurrected messiah" appeared to them: "When they saw him, they worshiped him; but some doubted." Matt 28:17.
Can you imagine that the authentic messiah appears to you and you still doubt?
Apparently he was not so authentic.
If the disciples, who saw the "resurrected Christ" with their own eyes, still doubted, why then do the Christians 2000 years later, who have nothing to go by but stories, don't doubt?