What indication is there that the famous census under Quirinius is the first-ever done in the region?

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.

A correct interpretation of Luke 2:2 requires taking into account a key item of historical information of a most practical nature: any census of subjects (as opposed to citizens) of the Roman Empire was carried out for tax purposes, to determine the taxable base of each subject. In such a census, people to be registered were not expected to travel but to do exactly the opposite: stay in their homes and wait for the census officer, who was above all a tax assessor. Josephus, in his description of precisely the census ordered by Quirinius in 6 AD, explicitely states that the registered people had their possessions assessed, including land and livestock (AJ 18.1-3, quoted in the Jul 20, 15 answer by Dick Harfield). And it is evident that Joseph did not have properties in Bethlehem, otherwise he and Mary would not have had to seek shelter in a manger for Mary to give birth.

Therefore, the historically informed translation of Luke 2:2: "hautē apographē prōtē egeneto hēgemoneuontos tēs Syrias Kyrēniou" is "this registration took place before Quirinius was governing Syria". Note that rendering "prōtē" as "before" is consistent with the established translation of the end of Jn 1:15: "hoti prōtos mou ēn" = "because He was before me".

Thus, noting from Acts 5:37 that Luke was fully aware of the event of Quirinius' census, its nature and its consequence, namely the uprising of Judas the Galilean, the reason of his mentioning the event in Luke 2:2 becomes crystal clear: state for the record that he was not talking about that census. I.e., Luke is saying: "Given that in a Roman census of imperial subjects people remain at their homes, I state for the record that the census that prompted Joseph and Mary to travel to Bethlehem was before Quirinius ordered his infamous one."

How then could it come to pass that Luke's statement was interpreted for centuries in exactly the opposite way as he meant it? Because of complete unawareness of historical context. I imagine that anyone living in the Roman Empire at that time would find this discussion hilarious to the point of ridiculous, and think: "How can these guys not understand that a census of subjects of the Empire (as opposed to Roman citizens) is for tax purposes, and that people must wait for the census officer at their homes? How else could the census officer reckon the taxable base of each person other than having a look at his property?"

On the other hand, the census that prompted the travel of Joseph and Mary was ordered by Herod and obviously restricted to the territory ruled by him. It approximately coincided in time with a global census ordered by Augustus in 8 bC, but was of different nature. Whereas Augustus' 8 bC global census was restricted to Roman citizens and for statistics, not tax, purposes [1], the motive of the Census ordered by Herod in 7/6 bC was that all his subjects should swear fidelity to Caesar and King (AJ 17.42) [2]. Together with the record of the oath, people were registered for an egalitarian contribution per capita in the way ordered by Ex 30:11-16, in which the possessions of each person were not taken into account.

In the context of a registration ordered by Herod, and knowing his profile, the order that all descendants of King David should register in one place was wholly plausible and logical, as it allowed Herod to know all potential claimers to the throne of Israel (and hence potential threats to his position). Furthermore, it is highly likely that the duty to travel to the city of their ancestors was in force only to King David's descendants, because of the people in general Luke says that "all went to be registered, each to his own town" (Lk 2:3), not "each to the town of his ancestors".

[1] Res Gestae Divi Avgvsti Chapter 22 (The Deeds of Divine Augustus) translated by Thomas Bushnell, BSG. Available online at: http://classics.mit.edu/Augustus/deeds.html#71

[2] Armand Puig i Tàrrech, "Jesus: An Uncommon Journey : Studies on the Historical Jesus", Mohr Siebeck, 2010. Chapter 2 "The Birth of Jesus", Section 4 "A More Judaico Census Decreed by Herod", pp 74-84. Partially available online at: http://books.google.com/books?id=elFp5tRSUH0C