We know from reading Acts 2 and 3 the kinds of things that happen when Peter preaches. As he is preaching the Gospel – he doesn’t even get to finish his sermon – the Holy Spirit falls on the Gentiles gathered in Cornelius’s house. Peter and those with him witness the manifestation of the Spirit as the Gentiles begin speaking in tongues. Peter sees no reason they should not be baptized “having received the same gift” as the Jewish believers.
This marks a major turning point in New Testament church history. Just like with the conversion of Saul, the news will require some convincing with the Apostles back in Jerusalem.