Since Peter is talking to a Gentile then I don't quite follow you.
Not all Gentiles in the Bible are the same. Cornelius was a blesser (Genesis 12:3 KJV) and as such his prayers and his alms came up for a memorial before God (Acts 10:1-4 KJV).
In any case, the full account of his message has:
The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all 37That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached; 38How 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. 39And 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: 40Him God raised up the third day, and shewed him openly; 41Not to all the people, but unto witnesses chosen before of God, even to us, who did eat and drink with him after he rose from the dead. 42And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead. 43To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
What Peter preached:
Acts 10:35 But in every nation he that feareth him, and worketh righteousness, is accepted with him.
This is contrary to what Paul preached
Titus 3:5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;
Peter preached the gospel of the kingdom to Cornelius’ house:
Acts 10:36 The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all
Acts 10:37 That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached;
Acts 10:38 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.
Peter delivers the murder indictment, but that God raised Christ up just as he preached in Acts 2 and 3
Acts 10:39 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:
Acts 10:40 Him God raised up the third day, and shewed him openly;
Acts 10:41 Not to all the people, but unto witnesses chosen before of God, even to us, who did eat and drink with him after he rose from the dead.
And it's all about the name (Matthew 16:15-18 KJV, the book of John) and please notice that through His name whosoever believeth on Him shall receive remission of sins. That is consistent with the gospel of the kingdom.
Acts 10:42 And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead.
Acts 10:43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
Peter's usual order of business was to deliver a murder indictment and preach a baptism of repentance for the remission of sins (not forgiven all trespasses like Paul (Colossians 2:13 KJV) and in so doing they shall receive the gift of the Holy Ghost. (Acts 2:36-38 KJV), but before he could finish his usual, the Holy Ghost fell on all them which heard the word.
Acts 10:44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.
Acts 10:45 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.
Acts 10:46 For they heard them speak with tongues, and magnify God. Then answered Peter,
my note:They were astonished at what happens because it was out of order of usual sequence as to when the Holy Ghost fell on them, but what does Peter do? He continues to preach what he knows and that's water baptism in the name of the Lord.
Acts 10:47 Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?
Acts 10:48 And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
He doesn't tell them the good news of our salvation (1 Corinthians 15:1-4 KJV); that "Christ died for our sins" as Peter didn't even know that good news at that time. That good news was a mystery (Romans 16:25-26 KJV) and Paul tells us why (1 Corinthians 2:6-8 KJV). Peter didn't tell them that what he was preaching was the gospel "by which also ye are saved" as Paul declared to us in 1 Corinthians 15:2 KJV.
Peter preached a future salvation for himself and those of Corne's house in accordance with the gospel of the circumcision ("shall be saved" Acts 2:20-21 KJV, "should be saved" Acts 2:47 KJV, "we shall be saved, even as they" Acts 15:11 KJV, 1 Peter 1:9-13 KJV ). So, Cornelius and his house heard what Peter preached, but there is no gospel of Christ to be believed there as the church which is His Body is NOT in the picture.