When did this idea start circulating. The writings that we have are long after the event would have taken place. If someone would have actually attempted the idea it would give a good reason as to why a story started being copied so much and given so much acceptance.
Don't get me wrong I think it is much more likely the writers did it themselves based off of some great philosopher. Either way someone had the idea to take all the stories of the jewish texts and turn them into something that nobody thought of before and it was fairly elaborate the way they pieced it together. It seemed very planned and schemed whether or not someone actually attempted the miracles. But how easy would it have been for someone to just say 'guess what my mom was a virgin when she had me, praise god'. Then again that whole "virgin" thing probably mistranslated but you get the idea.
There is one problem with that idea. We are talking about writings that occurred around 40 years at earliest. We can skip Paul for this as he tells us little about Jesus.
That is some time for those writers, after hearing the stories, to look back into their scripture and find texts that supposedly backed up their writing. That is actually exactly what happened.
We will take the idea of the virgin birth. Our earliest sources actually don't speak of it (Mark and Paul). Matthew and Luke disagree about the actual story. So it is unlikely Jesus ever said he was born of a virgin, or that the idea was circulating during his life.
However, we know that at sometime the story was created and began to circulate. Matthew takes the story, and claims that it was predicted in the OT. He says that Isaiah had stated it would be a Messianic expectation. However, if one looks at the passage, it never states anything about the Messiah. More so, if taken in context, one would see that the prophecy spoken of in the passage had already been fulfilled.
So what do we have? Someone after the fact, taking the life of Jesus, and trying to place it into the OT. If one looks at the various prophecies that Jesus supposedly filled, one will see that they have nothing to do with the Messiah, nor mention the Messiah.
So it isn't that Jesus was trying to fit into a character that is described in the OT. Instead, Jesus did things, grew a following, that following believed he was the Messiah, and then later on, searched the scripture to find ideas that could be molded into the life of Jesus.
It was only after the death of Jesus that those so called prophecies began to be searched out.