As to this salvation, the prophets who prophesied of the grace that would come to you made careful searches and inquiries, seeking to know what person or time the Spirit of Christ within them was indicating as He predicted the sufferings of Christ and the glories to follow. It was revealed to them that they were not serving themselves, but you, in these things which now have been announced to you through those who preached the gospel to you by the Holy Spirit sent from heaven—things into which angels long to look. (1 Pet 1:10-12)
“Peter, however, does not press the privileged status of his readers. Rather, he builds on the unity of the OT prophetic message with the Christian gospel as an apology for the cross and a foundation for his exhortations that follow. It does not appear that it was primarily Peter’s knowledge of the OT prophecies that led him to the Messiah. Rather, it was actually seeing and hearing Jesus. But after he recognized Jesus as the Messiah on the basis of Jesus’ teachings and miracles, the prophets’ forewitness provided a biblical basis that helped Peter later come to grips with the necessary suffering and death of the Messiah, the very concept he had once so resisted as unthinkable (Mark 8:31–33). By witnessing to the sufferings of the Messiah before they happened, the prophets provide a confirming forewitness that a crucified man would indeed be the long-awaited Messiah.
Peter knows his readers also needed to understand what he himself had come to know: that the suffering and death of Jesus Christ was not an untimely accident or tragic mistake but rather a necessity that had long been foretold. After the Christ has suffered, the predictive aspect of prophecy recedes, and the prophecy becomes a confirmation for the benefit of the generation who would see the Messiah suffer, and for the generations to follow them, that they might rightly understand the cross of Jesus. They need to know that the foreseen suffering of the Messiah necessarily preceded the expected glory of the Messiah. Peter extends this concept to develop the idea that as followers of Christ, his readers should therefore not be surprised when they, too, suffer (1 Pet. 4:12). Their sufferings for the name of Christ unite them to the experience and purposes of their Lord.” (Jobes, Karen. 1 Peter, BECNT, 103-104.)