Is repentance about saying sorry to God for making mistakes? No.
When Cornelius was the first gentile to be saved the Jewish believers said this:
Acts 11:18 “18 When they heard these things, they held their peace, and glorified God, saying, “Then God has also granted to the Gentiles repentance to life!”
What was his repentance that gave him salvation? Was it Cornelius confessing his sins or crying and pleading to God? No, it was simply believing in Jesus to receive forgiveness of sins!
Acts 10:43-45 “43 All the prophets testify about JESUS, that through his name everyone who believes in him will receive remission of sins.” 44 While Peter was still speaking these words, the Holy Spirit fell on all those who heard the word. 45 They of the circumcision who believed were amazed, as many as came with Peter, because the gift of the Holy Spirit was also poured out on the Gentiles.“
When John the Baptist preached repentance to Israel, it was about turning away from sins committed under the law to have faith in Christ (Mark 1:4-8). This specific repentance was because Israel was under the Law.
But for the Gentiles not under the law, the repentance was about turning to the TRUE GOD. The Gentiles were under the sin of worshipping other gods – in other words their sin was unbelief – because they were not under the law.
So the repentance of Gentiles is simply FAITH in CHRIST as Paul told pagans in Athens to turn from worshipping idols to the TRUE GOD who created all things and sent Jesus to save us:
Acts 17 ” I announce to you. 24 The God who made the world and all things in it, he, being Lord of heaven and earth, doesn’t dwell in temples made with hands. 25 He isn’t served by men’s hands, as though he needed anything, seeing he himself gives to all life and breath, and all things. 26 He made from one blood every nation of men to dwell on all the surface of the earth, having determined appointed seasons, and the boundaries of their dwellings, 27 that they should seek the Lord, if perhaps they might reach out for him and find him, though he is not far from each one of us. 28 ‘For in him we live, move, and have our being.’ As some of your own poets have said, ‘For we are also his offspring.’ 29 Being then the offspring of God, we ought not to think that the Divine Nature is like gold, or silver, or stone, engraved by art and design of man. 30 The times of ignorance therefore God overlooked. But now he commands that all people everywhere should repent, 31 because he has appointed a day in which he will judge the world in righteousness by the man whom he has ordained; of which he has given assurance to all men, in that he has raised him from the dead.”
This repentance of Gentiles is their turning to the TRUE GOD – the Lord Jesus Christ.
Acts 15 “19 Therefore my judgment is that we don’t trouble those from among the Gentiles who turn to God,”
This repentance is the great faith of another Gentile here:
Luke 7 ” 6 Jesus went with them. When he was now not far from the house, the centurion sent friends to him, saying to him, “Lord, don’t trouble yourself, for I am not worthy for you to come under my roof. 7 Therefore I didn’t even think myself worthy to come to you; but say the word, and my servant will be healed. 8 For I also am a man placed under authority, having under myself soldiers. I tell this one, ‘Go!’ and he goes; and to another, ‘Come!’ and he comes; and to my servant, ‘Do this,’ and he does it.” 9 When Jesus heard these things, he marveled at him, and turned and said to the multitude who followed him, “I tell you, I have not found such great faith, no, not in Israel.”
If you believe in Jesus then this is what he tells you
“Your sins are forgiven….Your faith has saved you; go in peace.” Luke 7:48,50
Repentance is the turning to Christ to have faith in him to be eternally saved by grace !