What indication is there that the famous census under Quirinius is the first-ever done in the region? Besides Luke's Gospel (which is grammatical difficult and may not mean "first" chronologically, but rather "most prominent/important"), is there any evidence that the famous census conducted by Quirinius in c. 6 AD was the first census taken in Judea under Roman rule?  Do any extant documents from antiquity state this or is the conclusion drawn largely from Luke and an argument from silence.  (Certainly there are known Roman registrations that could have extended into Judea (and don't necessarily relate to taxes), but we don't have a document that says they did.)  

The reason I ask is that people sometimes emphatically state that the 6 AD census was the first and thus Luke must be wrong to tie it to Jesus' birth.  (Whereas grammatically it is possible that Luke is saying "the census before that one".) I am just wondering if there is any hard data behind this statement, or if it as exactly as it appears - an overstatement of the confidence with which we know this "fact".
Until the time of Quirinius, Rome certainly had the power to impose a census in Judea, but to have done so would not have made any sense, being a waste of resources and an imposition on King Herod who ruled autonomously on Rome's behalf. After Herod's death, his empire was broken up, in accordance with his will, and Archelaus inherited Judea, Samaria and Idumea. Archelaus proved to be both unpopular and incompetent, so was deposed by Rome in 6 CE, with Rome taking direct control over the former kingdom. Rome now needed to know what taxes could be raised in its new provinceand therefore conducted a first Roman census in Judea. Josephus, the first-century Jewish historian,  reports as follows on Quirinius and his census:


  Jewish Antiquities , XVIII, i, 1: Quirinius, a Roman senator who had proceeded through all the magistracies to the consulship and a man who was extremely distinguished in other respects, arrived in Syria, dispatched by Caesar [Augustus] to be governor of the nation and to make an assessment of their property.  Coponius, a man of equestrian rank was sent along with him to rule over the Jews with full authority.  Quirinius also visited Judaea, which had been annexed to Syria, in order to make an assessment of the property of the Jews and to liquidate the estate of Archelaus; but the Jews, although at the beginning they took the report of a taxation heinously, yet did they leave off any further opposition to it ...


We can be certain of the date of this census, because Josephus actually mentions the year 6:


  Jewish Antiquities , XVIII, ii, 1: Quirinius had now liquidated the estate of Archelaus; and by this time the registrations of property that took place in the thirty-seventh year after Caesar's defeat of Antony at Actium were complete. Since the high priest Joazar had now been overpowered by a popular faction, Quirinius stripped him of the dignity of his office.


Luke 2:2 says that the census first (πρώτη) took place when Quirinius was governing Syria. The straight-forward reading of this, accepted by most scholars, is that Luke is saying this was the first census in the region.

Luke confuses things a little, by saying (Luke 2:1) that the census was necessary so that the whole world could be registered, thus intimating that the census involved the entire Roman Empire. However, there never was a census of the entire Roman Empire. In any case,  people throughout the Roman Empire, apart from residents of Rome, were already taxed long before the New Testament events.  Judea was being brought into the empire and preparations were being made to tax its population.