Peter wasn't even preaching to Cornelius actually. He was not expecting God to save Gentiles during that time since national Israel has not accepted their Messiah yet. That was why he never gave any call to Cornelius to "repent and be baptized".
He was just giving Cornelius a summary of what he has been doing with the Jews.
He was just giving Cornelius a summary of what he has been doing with the Jews.
Acts 11:13-17
"And he shewed us how he had seen an angel in his house, which stood and said unto him, Send men to Joppa, and call for Simon, whose surname is Peter;
Who shall tell thee words, whereby thou and all thy house shall be saved.
And as I began to speak, the Holy Ghost fell on them, as on us at the beginning. (The Jews received the Holy Ghost first as well)
Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost.
Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?"
Peter spoke the message, God filled the group, therefore Peter's statement above about not withstanding God had to do with offering to water baptize them in Jesus' name. (See below)
Acts 10:47-48
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.
Because Cornelius loved and feared the Lord, He actually sent an angel to tell Cornelius how to be saved. Loving, fearing, giving alms, and praying to God always would not gain him entrance into heaven. God sent Peter with the NT message of salvation.
Acts 10:1-4
There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band,
A devout man, and one that feared God with all his house, which gave much alms to the people, and prayed to God alway.
He saw in a vision evidently about the ninth hour of the day an angel of God coming in to him, and saying unto him, Cornelius.
And when he looked on him, he was afraid, and said, What is it, Lord? And he said unto him, Thy prayers and thine alms are come up for a memorial before God.