Why did Peter and the apostles in early Acts only use the Old Testament program?
Peter and the apostles operated only on what God had already revealed, which was the Old Testament program. They had no concept of God turning to the Gentiles for 1900 and some years. This was not their fault, because God had kept that purpose secret and was still giving Israel opportunity to repent.
Les explains that during the early chapters of Acts, Peter is not talking to the Church or to Gentiles. The Church, the rapture, and Church doctrine or the Gospel as we know it are not found in the Gospels or the Old Testament, because they were a secret held in the mind of God. God was dealing only with the nation of Israel, offering the King and the Kingdom. Israel kept rejecting that offer, so God moved the program into the future and inserted an undetermined period of time. Peter and the eleven could only act on what God had revealed: the Old Testament program. They had no idea God would turn to the Gentiles for 1900 and some years. It was not their fault, and God did not expect them to know, because He had been holding it secret while giving Israel every opportunity to repent.