A few things.
1.) We can’t really say definitively that the theory that the idea of Jesus as divine could not have arisen within a Palestinian Jewish context.
See, in 1st century Judaism, there was a concept of certain angelic or human (usually historical / scriptural) figures being exalted by God and honored with such high positions that they can sometimes be described as being in a way, almost God-like. (Scriptural support for such a concept can arguably be found in the exaltation of the ‘one like a son of man’ in Daniel 7.)
There is still one God, but just beside him is another somewhat semi-divine figure, a ‘divine agent’ who is thought to share in certain ways God’s authority and high position but usually not necessarily without being a sort of second god himself, whether an angel like Metatron or Michael, some eminent patriarch or prophet like Enoch or Moses, or even personified divine attributes such as Wisdom and the Logos (the ‘Word’ of God).
We see certain similarities here with early Christian thinking about Jesus - that He was raised from the dead and exalted by God, that He is given a name above every other name, that He is seated at God’s right hand, all that.
But at the same time, the pattern we see in Jesus is different from what we see in these other ‘divine agent’ figures. Whereas these other ‘divine agent’ figures were never worshiped by Jews or explicitly given divine attributes, in the case of Jesus we see a kind of devotion directed towards Him from the earliest times: hymns celebrating His resurrection, prayer to Jesus, belief in the power of the name of Jesus, baptism in the name of Jesus, the Lord’s Supper (Eucharist), the confession of Jesus as ‘Lord’ or ‘Son of God’ or ‘Christ’, and prophetic statements attributed to the risen Jesus. According to Larry Hurtado, this ‘mutation’ in the pattern may have occurred due to experiences the followers of Jesus had which led them to see Him not just as a mere divine agent, but also as Lord, Kyrios (the same term that translates the Name Yhwh in the Greek Old Testament) and Savior.
2.) Miracles do not necessarily divinity make. There were a lot of ‘miracle-workers’ and ‘wonder-workers’ in Jesus’ time, even among the Jews - He was just one of many (cf. Honi (Onias) the Circle-drawer). And even those who are deemed to be ‘authentic’ (rather than charlatans) were simply thought of as humans who have a special, intimate relationship with God, not necessarily a ‘son of God’ (as we Christians understand the term), much less God in the flesh.
So it was actually not so much the miracles and the healings, but rather the death and the resurrection (emphasis on ‘resurrection’) of Jesus that caused His followers to have an exalted view of Him. Jesus’ earthly ministry was anointed by God, but it is by virtue of God’s resurrection and exaltation of Jesus that Jesus is now called “Lord and Christ,” the judge and the one valid medium of salvation (Acts 2:32-36; 10:40-43; Philippians 2:5-11; 1 Corinthians 15:20ff; 1 Peter 3:22; etc.) In other words, we can say that the empty tomb is key to the rise of high Christology: if the belief that Jesus was not raised from the dead did not arise, Jesus would have simply been another holy man, another prophet, but not exactly someone who is Lord and co-sharer in the glory of God the Father.
3.) Which brings us to the issue of the idea of Jesus’ pre-existence, something that is also seen as early as the writings of St. Paul. Larry Hurtado:
But how could people ascribe a heavenly “pre-existence” to a real human and mortal figure of recent history? To understand this, you have to enter into the “logic” of ancient theological thought, and especially “apocalyptic” thought. I’ll sketch it briefly. God doesn’t make up his game-plan as the game goes along, but has the plan (of world history, redemption, judgement, etc.) all laid out even before creation. So, as God acts in revelation, each action is also an unveiling of his prior purpose and plan. So, “eschatological” events were actually in God’s purpose from the beginning: “final things = first things” (to paraphrase a scholarly formula). Indeed, in ancient Jewish texts there are references to various things, e.g., Torah, or the “name” of the messianic figure in the “Parables” of 1 Enoch (37-70) as “pre-existent” (see, e.g., my article, “Pre-Existence,” in the Dictionary of Paul and His Letters, eds. G.F. Hawthorne, et al., pp. 743-46 (and bibliography there).
So, in this case, if Jesus has been vindicated by God and exalted to heavenly glory, made Lord and judge, declared to be “the Son of God,” and the unique redeemer, then in some sense this is the eschatological revelation and articulation of what must have been God’s purpose, and the revelation of heavenly realities, from before creation. As various other scholars as well have observed, the conviction that Jesus had been exalted to heavenly/divine glory seems to have triggered the logical corollary that he must, in some sense, have been “there” from the beginning, and that God’s redemption work is tied closely to God’s creation work. (Note that NT statements about Jesus’ “pre-existence” are essentially confined to connecting him to creation, and there is scant interest in speculations about what else his “pre-existence” involved. There, isn’t in other words, the proliferation of elaborate “myth” narratives about the matter such as we have in the classic Greek myths of the gods.)
But despite ascribing pre-existence or divine honor to Jesus, the NT doesn’t insinuate that Jesus was somehow un-human. Instead, Christians were at pains to show that Jesus was a real, mortal, human being, not a divine spirit who wore human flesh like a set of clothes.