How did the disciples suddenly come to understand the Old Testament prophecies about Jesus?
Jesus Himself opened their understanding so they could comprehend the Scriptures. It required a sovereign act of God, not merely human reasoning. When He ordained that they understand, the lights came on, and they began to see the whole Old Testament program unfolding concerning Him.
Jesus told them these were the words He spoke while He was with them, that all things written in the law of Moses, in the prophets, and in the Psalms concerning Him must be fulfilled. Then He opened their understanding that they might understand the Scriptures. Les emphasizes that it took an act of God; when He sovereignly ordained that they should understand these things, all of a sudden the lights came on, and they began to see the whole Old Testament program as it had been unfolding. Les also notes there is still no hint of the church age or of God going to the Gentiles except through this prophetic program, confined to the 490 years, 483 up to the cross.