Let’s look at this another way. Compare other religions and cults. Mormonism was started by a single author who wrote a single book and everything is derived from it. Islam has a single author. Scientology (yes, for the purposes of this discussion, it qualifies) was derived from Dianetics and other works by a single author.
Because of the more recent authorship, we can confirm (or refute) much of what’s written, or at least who wrote it. Older works have a worse time. Consider when rabbis sit down to discuss that the Torah means; their sole source of inspiration is the Torah. AFAIK, they don’t cross-reference it with Egyptian documents of the time to interpret what God wants.
What if…some prophet, seer, or just wacky, fantasy-prone crackpot, drawing from other stories (Osiris, etc.) and local legends, some with a grain of truth, sat down and wrote Q, or something much like it? The story was passed around, either on parchment, papyrus, scroll, or word of mouth, becoming elaborated, augmented and distorted in the process. It developed a following, a mind of its own, became a meme. It was believable at the time and was eagerly adopted with little question by the gullible. Perhaps it filled a need for those who were searching and had a mental or social void to fill.
Much like followers of Nostradamus, scribes/priests/believers searched for and found references in older works (Old Testament) that seemed to predict this new story. If they didn’t match perfectly, the new story was altered to fit, or new sections added to “fulfill” a prophecy. Data was added when copies were made. This could explain the birth story and other episodes that were not in the earlier works.
Perhaps you find this preposterous. I don’t, as I see something like this happening every day. Think of how many times The Onion is treated as a valid news source. Urban legends abound. The Protocols is treated as a genuine document for world conquest; Report From Iron Mountain is believed by some to be a serious plan to perpetuate war.
We can refute these with our modern tools, yet some don’t accept the refutation, and certainly these tools were lacking in the First Century.
I find much to suggest that such a scenario could have happened. Is there anything we know that would strongly disconfirm my proposed scenario?
As an example of disconfirming evidence, suppose we can show that parts of the Jesus story came from a source that could not possibly have had any contact with the writer(s) of Q or the first NT books.