Matthew 28: 16 Then the eleven disciples went to Galilee, to the mountain where Jesus had told them to go. 17 When they saw him, they worshiped him; but some doubted. 18 Then Jesus came to them and said, “All authority in heaven and on earth has been given to me. 19 Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, 20 and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.”
Mark 16: 15 He said to them, “Go into all the world and preach the gospel to all creation. 16 Whoever believes and is baptized will be saved, but whoever does not believe will be condemned. 17 And these signs will accompany those who believe: In my name they will drive out demons; they will speak in new tongues; 18 they will pick up snakes with their hands; and when they drink deadly poison, it will not hurt them at all; they will place their hands on sick people, and they will get well.” 19 After the Lord Jesus had spoken to them, he was taken up into heaven and he sat at the right hand of God. 20 Then the disciples went out and preached everywhere, and the Lord worked with them and confirmed his word by the signs that accompanied it.
Acts 1: 7 He said to them: “It is not for you to know the times or dates the Father has set by his own authority. 8 But you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth.”
So Matthew says it; Mark says it; Luke says it in Acts (and John omits it). All the earth. All nations. All men. Not just the Jews.
The Jewish Christians that were forced to flee from the persecution of Acts 8:1,2 went into Phenice, Cyprus, and Antioch establishing Christian Churches to all, including Gentiles...uh, no, that's not right...they established JEWISH churches.
His first six epistles are full of miracles, signs and wonders (Acts 19:12) and legal ceremonies (Acts 16:3,4), "because of the JEWS" (Acts 16:3). (cf. 1 Cor. 9:20-23; 10:32). Those epistles would be 1 and 2 Thessalonians, Galatians, 1 and 2 Corinthians, and Romans.
BUT AFTER Israel is blinded and set aside, Acts 28, he no longer preaches or practices things that are Jewish. The Gospel is preached to the nations WITHOUT RACIAL PRIORITIES (Eph. 2:11-22; 3:6), WITHOUT MIRACLES, SIGNS, and WONDERS (1 Tim. 5:23, 2 Tim. 4:20; Phil 2:25-29) and WITHOUT LEGAL CEREMONIES (Phil. 3:8-14).
Ephesians, Colossians, Philippians, Philemon, 1 and 2 Timothy, and Titus would be those epistles AFTER Israel is set aside. So to say that Paul stayed within Jewry is only partly right. As long as Israel was operational and could have accepted Christ as Messiah, Paul went to the Jew first, as a minister of confirmation to the Jews concerning Jesus, the promised Messiah. (Acts 13:14-41; 18:5; 26:22, 28:23).
But he also had a ministry of revelation. The Apostle to the Gentiles, The dispensation of the grace of God, the Church the Body of Christ, the One New Man, the fellowship of the mystery (Eph. 3:9). All by direct revelations to him from the risen Christ, beginning in Acts 9.
unless you just believe him to be just a really good salesman...