Why should we expect to see Jesus in the Old Testament? The simple answer is that this is how the New Testament teaches us to read it. Recall the words of Jesus on the road to Emmaus. On that occasion, Jesus caught up with two despondent disciples who were leaving Jerusalem after the crucifixion, unaware of the resurrection. As they walked in the gathering gloom of evening, He took them on a tour of the Old Testament Scriptures, exposing their woefully inadequate knowledge and understanding by saying,
“O foolish ones, and slow of heart to believe all that the prophets have spoken! Was it not necessary that the Christ should suffer these things and enter into His glory?” And, beginning with Moses and all the prophets, He interpreted to them in all the Scriptures the things concerning Himself. (Luke 24.25-27)
In other words, Jesus unfolded the Old Testament, showing them how it is fulfilled in Him. According to Jesus, we should expect the message of “Moses and all the prophets” (that is, the whole of the Old Testament) to be Jesus Christ. Notice, too, that the disciples’ response was not to be amazed at His cleverness in uncovering references to Himself in such a wide range of sources. Rather, they were astonished at their own dullness in not having recognized before what these familiar books were about.
From: Is Jesus in the Old Testament? by Iain M. Duguid (Philadelphia: Westminster Seminary Press/Phillipsburg: P&R Publishing, 2013), pp. 8-9.