God sent Peter to the Gentiles
Acts 10:24-26 And the following day they entered Caesarea. Now Cornelius was waiting for them, and had called together his relatives and close friends. As Peter was coming in, Cornelius met him and fell down at his feet and worshiped him. But Peter lifted him up, saying, "Stand up; I myself am also a man."
Christians then were only Jewish converts whose basic foundation was Judaism. With their belief that Gentiles were unclean, it would be impossible for these Christians (Jewish converts) to reach the Gentiles with the gospel.
After God had convinced Peter to change his understanding and to meet up with Cornelius the Roman Centurion, he was surprised that Cornelius fell down to worship him.
Acts 10:28-29 Then he said to them, "You know how unlawful it is for a Jewish man to keep company with or go to one of another nation. But God has shown me that I should not call any man common or unclean. Therefore I came without objection as soon as I was sent for. I ask, then, for what reason have you sent for me?"
Gentiles Ready to accept Gospel
Act 11:13-14 And he told us how he had seen an angel standing in his house, who said to him, 'Send men to Joppa, and call for Simon whose surname is Peter, who will tell you words by which you and all your household will be saved.'
When Peter heard that an angel had told Cornelius that he would bring the message that could save him and his family, then he realised that all these Gentiles were ready to believe and accept anything he said.
So Peter started to preach the gospel of Jesus to them knowing that all of them would readily accept it
Act 10:34-35, 38-40, 43 Then Peter opened his mouth and said: "In truth I perceive that God shows no partiality. But in every nation whoever fears Him and works righteousness is accepted by Him... how God anointed Jesus of Nazareth with the Holy Spirit and with power, who went about doing good and healing all who were oppressed by the devil, for God was with Him. And we are witnesses of all things which He did both in the land of the Jews and in Jerusalem, whom they killed by hanging on a tree. Him God raised up on the third day, and showed Him openly,.. To Him all the prophets witness that, through His name, whoever believes in Him will receive remission of sins."
Gift of the Holy Spirit to Gentiles
Act 10:44-48 While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word. And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also. For they heard them speak with tongues and magnify God. Then Peter answered, "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?" And he commanded them to be baptized in the name of the Lord...
When the gift of the Holy Spirit fell upon Cornelius and family just like in Pentecost, Peter then believed that the Gentiles were also saved by the grace of God in Christ Jesus. Cornelius and family were then baptized.
Many Hellenists also Saved
Act 11:20-21 But some of them were men from Cyprus and Cyrene, who, when they had come to Antioch, spoke to the Hellenists, preaching the Lord Jesus. And the hand of the Lord was with them, and a great number believed and turned to the Lord.
In Antioch many Greek speaking Jews were saved. After Jerusalem had accepted that the grace of God was also extended to Gentiles, many more Gentiles were saved.