What proofs that the Jerusalem church held the same belief of St. Paul with regard to the crucifixion and resurrection of Jesus?

Question

Some critics of Christianity, (Muslims, for example), argue that though Saint Paul believed that Jesus was crucified and his crucifixion has a significance (that he redeems all people from the effects of the Fall) but that doesn't necessarily require that the Jerusalem church led by James and Peter, believed that Jesus was crucified and assuming that they did believe that Jesus was crucified, then that doesn't necessarily require that the Jerusalem church, believed that his crucifixion has a theological significance (atonement).

How can we be assured that The Jerusalem church did believe that Jesus was crucified and his crucifixion has significance?

Please Note: Answers should exclude any textual proofs from the Epistle of James.

Answer 1

Peter (Jerusalem Church)

On the day of the Pentecost (50 days after resurrection/Easter, 10 days after Ascension), Peter preached to the crowd about Jesus's crucifixion and resurrection, thus demonstrating that Peter (who represents the other 10 apostles) held the same belief as St. Paul, who came to believe later.

It is recorded in Acts 2.

Acts 2:32-36:

³² “God raised Jesus from the dead, and we are all witnesses of this. ³³ Now he is exalted to the place of highest honor in heaven, at God’s right hand. And the Father, as he had promised, gave him the Holy Spirit to pour out upon us, just as you see and hear today. ³⁴ For David himself never ascended into heaven, yet he said,

      ‘The Lord said to my Lord,
         “Sit in the place of honor at my right hand
 35   until I humble your enemies,
         making them a footstool under your feet.”’

³⁶ “So let everyone in Israel know for certain that God has made this Jesus, whom you crucified, to be both Lord and Messiah!”

As Peter's belief of the atoning significance of Jesus's death, see his letter 1 Peter, specifically 1 Peter 2:24:

He personally carried our sins in his body on the cross so that we can be dead to sin and live for what is right. By his wounds you are healed.

For more in depth discussion on Peter's view of the atonement, see book chapter First Peter and Atonement Theology by Greg Rosauer (part of the 2019 book For It Stands In Scripture: Essays in Honor of W. Edward Glenny).

Paul

Paul based his conviction that Jesus died and was raised again on his encounter with the living Jesus on the road to Damascus (Acts 9:1-31) as well as the personal testimony of 500+ people who saw that Jesus was alive (1 Cor 15:1-9):

¹ Let me now remind you, dear brothers and sisters, of the Good News I preached to you before. You welcomed it then, and you still stand firm in it. ² It is this Good News that saves you if you continue to believe the message I told you—unless, of course, you believed something that was never true in the first place.

³ I passed on to you what was most important and what had also been passed on to me. Christ died for our sins, just as the Scriptures said. ⁴ He was buried, and he was raised from the dead on the third day, just as the Scriptures said. ⁵ He was seen by Peter and then by the Twelve. ⁶ After that, he was seen by more than 500 of his followers at one time, most of whom are still alive, though some have died. ⁷ Then he was seen by James and later by all the apostles. ⁸ Last of all, as though I had been born at the wrong time, I also saw him. ⁹ For I am the least of all the apostles. In fact, I’m not even worthy to be called an apostle after the way I persecuted God’s church.