I wish to emphasize that the process we are discussing was not linear, but organic and dynamic. One idea brought with it a complex of other ideas and fairly quickly you get a new mosaic or collage of images and explanations developing around one figure. As the first Christian Jews were trying to sort out Jesus' death, this sorting had real implications for how they recalled and came to understand his life and teachings. Whether the manner in which they framed his ministry as the Prophet-like-Moses was actually how his ministry played out is doubtful, but there were likely bits and pieces of Jesus' life that they saw corresponded enough with the expectations of the Prophet-like-Moses mentioned in Deuteronomy 18:15-16 that this framing made sense to them. In other words, if Jesus himself didn't present himself as some kind of prophet, his very earliest followers did because it is multiply-attested in all the layers of the tradition. Clearly his followers didn't identify him with any ol' prophet. They hooked him into the traditions of the Prophet-like-Moses, who was a messianic figure within Judaism and especially Samaritanism. The idea was that during the last days the prophet would come to restore God's law to its original intent, and this would prepare the faithful for the final Judgment.
So we find stories of Jesus' baptism where the Spirit anoints him just as other prophets were anointed in the past (Wis. Sol. 7:27). For our upcoming discussion, it will be important to note that Mark portrays Jesus as a fully human being, whose soul has been augmented by the Spirit of God when he was possessed with the Spirit at his baptism.
The other very important factor here is that the Moses traditions were part of a larger complex of traditions in which the Jews were discussing their heroes as figures so righteous and loved by God that they were believed to be exalted and transfigured (i.e. Enoch, Jacob, Moses, etc). The Moses traditions are quite fascinating because Moses is given such an exalted status in heaven that he is pictured enthroned (on God's throne!) as God's viceroy and mediator. In Samaritan traditions, Moses is so exalted and glorified that he is even given God's divine Name. It is this willingness to exalt heroes, to enthrone them, to invest them with the divine Name, that helps us explain how and why Jesus gets associated with the divine Name too. Very early in the tradition, we have the confession "Jesus is Lord" which means "Jesus is YHWH" (i.e. 1 Cor 12:3; Phil 2:9-11; Rev 17:14; 19:16; Acts 2:38). Like any other idea, once the Name is associated with Jesus, so too is a number of other traditional complexes which I will discuss in an upcoming post.