What did Peter actually preach to Cornelius and his household?
Peter preached Jesus of Nazareth—crucified, raised from the dead, and alive—as the Messiah and Son of God. He declared that through His Name, as all the prophets witnessed, salvation was offered. He did not yet preach the cross-work gospel Paul later taught.
Les explains that Peter was in Cornelius's house, preaching to a Gentile household. Peter had not spoken of the work of the cross for salvation by Jesus's shed blood, as Paul would have done. Instead, Peter rehearsed that Jesus of Nazareth, who had appeared to Israel, was crucified, killed, raised from the dead, and alive. In Acts 10:43, Peter said all the prophets witness that through His Name—not through His work of the cross—salvation is given. Peter did not yet know Paul's Gospel, but he knew the Name of Jesus of Nazareth, the Messiah, the Son of God, was the vehicle for salvation. While Peter was yet preaching, the Holy Spirit came upon the Gentiles, evidenced with tongues, which flabbergasted Peter because he expected repentance, baptism, and then the Spirit.
That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached;
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Did Peter preach about the cross and Jesus' shed blood to Cornelius?
When Peter preached at Cornelius' house he had not said a word about the work of the cross for salvation by Jesus' shed blood, the way Paul would have done.