Acts 10 is important, because Peter has a vision from God and he takes the gospel and goes out to a Roman and baptizes his whole family and that includes his slaves. The Holy Spirit comes over the entire home.
The Gentiles, in the person of Cornelius and others, were formally welcomed into the church in Acts 10, this being prophetically revealed as prerequisite to the giving of the “new name” (Isaiah 62:2).
Gentiles could become part of the movement to follow Christ, without being coming Jewish first, but through believing in Christ, hearing the word, believing the word, repenting and becoming baptized. Amen.