I'm going to expand on my previous post:
On the face of it, the OT witness to a divine messiah is sparse. Yet there's heavy emphasis on the deity of Christ in the NT. How were NT writers able to bridge the difference? What made it so easy for NT writers to seamlessly transition to a divine messiah as the fulfillment of OT expectations? I submit that there are several converging themes:
1. Sonship is a theological metaphor. In the OT, this applies to Israel. In that application, sonship is a figurative, collective, and adoptive category. A metaphor for God treating the Israelites as if he was an adoptive father who rescued them and raised them.
However, once sonship as a theological metaphor comes into play, that carries a potential shift from figurative, collective, adoptive sonship to metaphysical, individual, analogical sonship.
2. It has the added advantage that fatherhood and sonship simultaneously represent similarity and difference. On the one hand there's the physical and psychological affinity between fathers and sons. On the other hand, these are distinct individuals.
3. In addition, the OT contains two or three repeated and related themes:
i) A king is coming
ii) God is coming (e.g. Day of the Lord)
iii) An heir to David's throne
These are pervasive theological themes. A sampling of passages includes Gen 49; Pss 2, 8, 72, 89, 110, 132; Isa 2, 7, 9, 11, 34; Jer 23, 30; Ezk 37; Dan 7, 9; Hos 3; Micah 5, Haggai 2, Zech 9.
4. The notion of royal succession explicitly or implicitly involves sonship. Ordinarily, a royal son is the king's successor.
In human terms, the reason for royal succession is mortality. Kings die of old age. Some kings die in battle.
Usually the royal son assumes the throne upon his father's death. Sometimes, however, to ensure that the crown will pass to the designated heir, a king will abdicate the throne or appoint his son as coregent. In other words, while the old king still holds the reins of power, he will use it to ensure the succession. The NT trades on this dynastic backstory.
And, of course, normally, fathers and sons exist on the same plane and domain. If a father is human, his son is human. Indeed, it's because fathers and sons are so alike that a son is the most natural successor to the throne. A natural extension and continuation of the old king.
If, however, the king is divine, then it's a short inference to the divinity of the crown prince. What was latent in the OT becomes patent in the NT.
5. On a related note is the coming of God motif. This typically depicts Yahweh coming in salvation and judgment to deliver his people and vanquish their enemies. And it dovetails nicely with the motif of a future Davidic king.
6. Critics might object that this can be satisfied by human agents who act in God's stead as his vice-regent. There are, however, problems with that explanation:
i) The coming of God passages suggest a climactic advent. Something that hasn't happened before. If, however, it refers to just another human representative, then that would be anticlimactic.
ii) Apropos (i), if it refers to just another human representative, then either Yahweh repeatedly comes in the person of his agent, or else he never really arrives–because an agent always takes his place. Again, though, the coming of Yahweh passages suggest something different from business as usual. Not just another human stand-in, but the culmination of promise, where human agents were merely proxies and precursors to the real deal.
iii) Apropos (i-ii), Israel had a series of kings. Even her best monarchs were notable failures. Wouldn't yet another human king be a major letdown? The golden age prophecies about the coming of God and the heir to David's throne envision something truly superlative.