Apart from a few loosely attached sections like all the birth narratives, moreover, I'm inclined to suppose that the New Testament is more a record of people's reaction to Jesus than something that later writers made up and projected on Jesus as a mouthpiece character. There may well be some of that, sure, but I think history includes a lot more examples of widespread meme clusters launched by one genius than it has of world religions launched by anonymous committee. Very likely the Jesus story accumulated extensions or distortions, but I think there must surely have been a core upon which they could accrete.
Something I still find fascinating about the New Testament, though, is how much it contains explicitly about the confrontation between the insular and religious culture of first-century Palestinian Judaism and the secular cosmopolitanism, mostly Hellenistic, of the whole first-century Roman Empire. The gospels even include a few interactions between Jesus and gentiles. One of the easiest to overlook might be the most important:
In John's gospel, it is this news that Jesus's message has started reaching "Greeks" that seems to trigger the whole Passion sequence.In John 12:20-22, the author of John wrote:Now there were some Greeks among those who went up to worship at the festival. They came to Philip, who was from Bethsaida in Galilee, with a request. “Sir,” they said, “we would like to see Jesus.” Philip went to tell Andrew; Andrew and Philip in turn told Jesus.
Some of the Jesus-with-Gentiles stories do seem to be told from a pretty Jewish point of view, looking down on the heathen, but even these do show Jesus himself willing to expand his mission to include Gentiles, praising their faith. So I think that just reading the New Testament makes clear that Christianity was a fusion of Judaism and Hellenism, from the beginning.
The point I want to make is that it wasn't an unconscious fusion in which Greco-Romans simply hijacked a Jewish movement and made it into something new. Christianity was a conscious and explicit fusion, and you can see a lot of the fusing already happening in the oldest Christian sources we have. The oldest surviving written sources of the New Testament are all in Greek, after all—not Hebrew or Aramaic.