*** It does not prove what you are saying. The Holy Spirit came up on Cornelius "while he(Peter) was still speaking". You can't be a Christian without belief,".***
I'm sorry my friend, but that argument doesn't hold up. The passage tells us what Peter had alread said...
"...how God anointed Jesus of Nazareth with the Holy Spirit and with power. He went about doing good and healing all who were oppressed by the devil, for God was with him. 39And we are witnesses of all that he did both in the country of the Jews and in Jerusalem. They put him to death by hanging him on a tree, 40but God raised him on the third day and made him to appear, 41not to all the people but to us who had been chosen by God as witnesses, who ate and drank with him after he rose from the dead. 42And he commanded us to preach to the people and to testify that he is the one appointed by God to be judge of the living and the dead. 43To him all the prophets bear witness that everyone who believes in him receives forgiveness of sins through his name."
Clearly they had heard the gospel... the very gospel as Paul defined it.
They believed what they heard and were instantly born again.
Your quotes here are from Acts 10, where Luke tells us everything that Peter said. In Acts 11, Peter is defending himself to the Jewish Christians, and he says that the Holy Spirit came upon them "as I began to speak". If he had just begun to speak, he had not finished saying everything that is recorded in Acts 10.