I believe Peter was saved the same way the rest of us are saved through believing in Jesus by faith. As for Cornelius he was also saved before he was baptized which is shown by his receiving the Holy SpiritHello,
I'm still wondering if you believe Peter could be saved without preaching the gospel that Jesus commanded him to preach? i.e. Mark 16:15-16
Also could Cornelius have been saved if he did not obey Peter's gospel commandment to be water immersed in the name of the Lord, Acts 10:47-48.