Did Peter understand anything beyond the Old Testament prophetic timeline?
No. According to the context, Peter had no concept of anything beyond the Old Testament prophetic timeline. The Gospels contain no word that God would turn to the Gentiles and call out a body of Christ from Jew and Gentile. Peter saw only the promised suffering, death, resurrection, wrath, and kingdom.
Les teaches that Peter had no concept of anything other than the Old Testament timeline. The Old Testament looked forward only to Christ coming, suffering, dying, being raised, then the wrath of God falling, and the kingdom being set up. At Pentecost in Acts 2, when accused of drunkenness, Peter responded that it was only the third hour, and explained what they were seeing as the fulfillment of prophecy. Nothing in the Gospels revealed God turning to the Gentiles to call out a body of Christ made up of Jew and Gentile.