How should we study passages where earlier Bible people did not understand what God was doing?
Study such passages with the understanding that God sovereignly kept secrets and revealed His plans only periodically. Earlier believers, like Peter and John in Acts 3, understood only part of God's purpose. Recognize that the secret things belong unto the Lord our God (Deuteronomy 29:29), so study Scripture expecting periodic revelation rather than assuming they knew later truth.
Les teaches that we should study Scripture knowing that God has not revealed everything at once. He says God over and over said, "I'm keeping this secret. I'm not telling you everything," and that only periodically does God reveal something that those people back there didn't understand. That is why Peter and John in Acts chapter 3 still had no understanding of what God would put on the death, burial, and resurrection of Christ. At that point they understood only that He was the Messiah, the Son of God, proven by His miracles, but only for the nation of Israel. God had not blanked the Gentiles out of His thinking; He would use the favored covenant nation to reach pagan, idolatrous Gentiles at the appropriate time, but Israel was dragging their feet, so that time had not come. Deuteronomy 29:29 states, "The secret things belong unto the Lord our God." Les notes that deity is capable of hiding things, and even the psalmist asked why God hides these things, but He is sovereign and has the right to do so. So we should not read later revelation back into earlier passages or assume earlier believers understood what God had not yet revealed; we study with the awareness that God reveals His purposes periodically according to His sovereign timing.