[A]rchaeology has confirmed a stone building in Nazareth of the size and type to be a synagogue, and it dates from the time of Christ. See the entry in the Archaeological Encyclopedia of the Holy Land...

The evidence is insurmountable that there were numerous permanent structures--most of Nazareth's buildings even before the 1st century were partially carved from the rock of the hill, in a manner similar to Pella...

I was able to track down on my own the most extensive report, that of Bagatti (Excavations in Nazareth, vol. 1, 1969), and I looked through all the subsequent reports on Nazareth from Excavations and Surveys in Israel, and this is what I found:

(a) Very little of Nazareth has been excavated, and therefore no argument can be advanced regarding what "wasn't" there in the 1st century.

(b) Archaeological reports confirm that stones and bricks used in earlier buildings in Nazareth were reused in later structures, thus erasing a lot of the evidence. Therefore, it is faulty reasoning to argue that there were no brick or stone structures simply because we have not recovered them from the relevant strata (i.e. one of Hoffman's sources assumed that the absence of this evidence entailed mud-and-thatch housing, but that is fallacious reasoning--especially since no clear evidence of mud-and-thatch housing has been found, either).

(c) One example of the above includes four calcite column bases, which were reused in a later structure, but are themselves dated before the War by their stylistic similarity to synagogues and Roman structures throughout 1st century Judaea, and by the fact that they contain Nabataean lettering (which suggests construction before Jewish priests migrated to Nazareth after the war). This is not iron clad proof of a 1st century synagogue (since the pieces had been moved and thus could not be dated by strata), but it does demonstrate a very high probability--especially since calcite bases are cheap material compared to the more expensive marble of structures archaeologists confirmed started appearing there around a century later, i.e. by the end of the 1st century AD (or early 2nd century at the latest, since marble fragments have been found inscribed in Aramaic that is paleographically dated to this period), and more extensively again in the 3rd century (when a very impressive Jewish synagogue was built there, this time using marble, which was later converted to Christian use).

(d) I confirmed beyond any doubt that Nazareth was built on a hill--more specifically, down the slope of a hill, with a convenient "brow" roughly one city block away from the edge of the ancient town as so-far determined archaeologically. Because the town was built down the slope of a hill, we have found numerous examples of houses, tombs, and storage rooms half cut into the rock of the hill, leaving a diagonal slope for structures to be built up around them to complete the chambers (as I described above). Since these structural elements were so completely removed and apparently reused by later builders, no evidence remains of what they were composed of (whether mud, brick, or stone).

The bottom line: there is absolutely no doubt that Nazareth existed in the time of Jesus.