Incredible the violence you do to the word. A third grader could read the account given of Cornelius and know that he belonged to the Lord, he had a close relationship with the Lord; of course he was regenerate, LONG before Peter was ever sent to him. Acts 10 is the beginning of combining the two folds of sheep into one Christ foretold of in Jn 10.
'Saved' does NOT mean regenerated, is not synonymous with the birth from above. The baptism of the Spirit is NOT the birth of the Spirit.
How could Cornelius be regenerated when he did not have the Holy Spirit?
Acts 11:15 And as I began to speak,
the Holy Ghost fell on them, as on us at the beginning.
16 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.
17 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?
The only persons who receive the Holy Spirit are those who believe on Jesus Christ. Cornelius did not have the Spirit until he heard the gospel from Peter, therefore he could not be regenerated.
To be regenerated literally means to be made "alive again", just as Jesus described the prodigal son when he repented and trusted his father to forgive him.
Luk 15:24 For this my son was dead, and is
alive again; he was lost, and is found. And they began to be merry.
Luk 15:32 It was meet that we should make merry, and be glad: for this thy brother was dead, and is
alive again; and was lost, and is found.
You can't go around redefining words. Regenerate means to "make alive" (generate) "again" (re).
That is what the word regenerate means. It does not mean to teach, or illuminate, or enlighten, or to convict, or any other thing. It means to make someone alive again. Of course, this means they were alive once before which completely refutes Original Sin, but that is another argument for another day.
Regenerate is synonymous with being "born again". This happens when you believe and all your sins are forgiven. You WERE dead in trespasses and sins, but now you have been forgiven and been made alive again.
Cornelius was a good man who loved God and did many good works, but he was a lost sinner just like every other man. When he heard the gospel he believed on Jesus Christ and was washed clean, receiving the Holy Spirit. This is when he was regenerated, not before.
You can't go around changing the meanings of words. Absurd.