*** Up until the 3rd century the early Christians...***
Interesting stuff BTW. Thanks for posting it!
You have to remember that the New Testament did not begin until the resurrection .
Cornelius knew as much as had been revealed to him, and he acted on his faith .
Was Abraham regenerate? What about Moses and Elijah?
(2Ki 2:11 And it came to pass, as they still went on, and talked, that, behold, [there appeared] a chariot of fire, and horses of fire, and parted them both asunder; and Elijah went up by a whirlwind into heaven.)
OT figures were saved by faith just as are men today, but they looked forward to the cross in faith , where we look back.
So indeed by faith Cornelius might have been righteous and pleasing to God as were all the OT saints ( and include John the Baptist and His parents in that )
But it was obviously of great import to God that he have the gospel , look at all the trouble He went to to provide it :)