Hello James,
I gather the passage in Acts 2:32-37 where Peter is preaching is one of those you refer to:
This Jesus God has raised up, of which we are all witnesses. Therefore being exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He poured out this which you now see and hear.
For David did not ascend into the heavens, but he says himself:
The LORD said to my Lord,
Sit at My right hand,
Till I make Your enemies Your footstool.
Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ.
Now when they heard this, they were cut to the heart, and said to Peter and the rest of the apostles, “Men and brethren, what shall we do?”
Cut to the heart by what? I think we see similarly in Acts 4:21ff after the release of John and Peter by the high priest and his council, as they met with their fellow believers and all prayed, and the place they were in was shaken and the Holy Spirit came upon them, in Acts 4:33 it is written,
And with great power gave the apostles witness of the resurrection of the Lord Jesus: and great grace was upon them all.
In both of these accounts we have the supernatural power of the resurrected Saviour manifest – "He poured out this which you now see and hear" (Acts 2:33).
Acts 4:33, with great power the apostles gave witness of the resurrection.
They were cut to the heart by the presence of the resurrected Saviour whose crucifixion they were parties to. They
saw Him with the eyes of their hearts. His glory, majesty, and love cut them deeply. This was the onset of their regeneration, and in their confusion, guilt, grief, and pain they asked Peter what should they do, and he said repent – turn from your dark hearts and ways to His light – for this is the promise to you and your children...
even as many as the Lord our God shall call.
By His appearing to them in His glory, Jesus was calling them to Himself. They were regenerated when the Lord appeared to them in the preaching of His resurrection. Even as ancient Abraham was regenerated when "The God of glory appeared unto our father Abraham, when he was in Mesopotamia" (Acts 7:2).
That's all it takes, the God of glory appearing to us, making us alive to Him in love.