The Gospel Is Preached

Acts 10:36-40 – The word which God sent unto the children of Israel, preaching peace by Jesus Christ (he is Lord of all). That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached.  How God anointed Jesus of Nazareth with the Holy Ghost and with power.  Who went about doing good, and healing all that were oppressed of 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 slew and hanged on a tree. Him, God raised up the third day, and shewed him openly.

The Gospel Is Obeyed And Gentiles are Born Again

Acts 10:44-48 – While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.  And they of the circumcision which believed were astonished, as many as came with Peter.  Because, that on the Gentiles also was poured out the gift of the Holy Ghost.  For they heard them speak with tongues, and magnify God. Then answered Peter, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?  And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.

Cornelius was a praying man however, he still needed to be born again by hearing, believing, and obeying the Gospel. How did Peter and his Jewish brethren know that the Gentiles had received the Holy Ghost? (Same way we do today).