Though this is only indirect evidence, we have the two conflicting Nativity stories in Matthew and Luke. Both of them go through rather embarrassing story-telling acrobatics to explain why Jesus really came from Bethlehem, even though he actually came from Galilee. If you invent someone out of whole cloth, and he's supposed to come from Bethlehem to fulfill the prophecy in Micah 5:2, then you simply have him come from Bethlehem. If, however, you're stuck with a real guy who came from Galilee, you then have to go through all these contortions to make him born in Bethlehem, so he can "fulfill" Micah 5:2.
Thus, I tend to see a historical Jesus around whom were wrapped myths of Jewish messianism and apocalypticism, as well as pagan hero myth motifs. The latter include Jesus turning water into wine - borrowed from the myth of Dionysus - and Luke's nativity, based on that of Hatshepsut and Egyptian pharaohs in general.
Uh, the city of Bethlehem was and still is in Galilee so your "explain why Jesus really came from Bethlehem, even though he actually came from Galilee" comment makes no blasted sense.
It is like saying you are going through story-telling acrobatics to say somebody was born in Gahanna, Ohio (a city) when they actually were born in Franklin Country, Ohio--you are ignoring the fact that Gahanna, Ohio (Bethlehem) is IN Franklin Country, Ohio (Galilee)

The real problem is Matthew is trying to claim fulfilled prophesies generally misunderstanding what the OT is really saying...when he bothers to even tell you where the supposed prophesy is coming from.
The problem with both "Bethlehem" and "Nazarene" in the OT is there is NOTHING to show they are places. Farrell Till points out in "Prophecies: Imaginary and Unfulfilled" that the "Bethlehem" in Micah 5:2 could just as easily refer to a clan.
The term "Nazarene" is even worse as you have two possible root words: "ne·tzer" and "na·zir"- the first meaning branch and the second meaning one consecrated, devoted (to God).
In fact, Pliny the Elder in his Historia Naturalis (Book V,22) talks about the Nazerini group that given the references existed in the 1st century BCE.
So the whole story-telling acrobatics were unnecessary unless what you have are several stories of various would be messiahs being woven together into one narrative. In short the Gospel Jesus is a composite character and not historical by definition as no one man did all these things.