How authentic is the Nativity Grotto in Bethlehem? It depends on what one means by "authentic". The historical Jesus was probably born in Nazareth, not Bethlehem. The earliest gospel, Mark, refers to him many times as "the Nazarene" and contains no birth account at all. It simply assumes that he was born in the same place where he spent his childhood. The two later gospels that do contain a Bethlehem birth scene, Matthew and Luke, clearly do so to imbue Jesus with the necessary Davidic qualities of the Messiah (cf. Micah 5:1). But these two gospels do not mention the birth taking place in a cave. Matthew says it was in a "house", while Luke mentions "a manger, because there was no place for them in the inn." The latter is the inspiration for the barnyard nativity scenes we are used to seeing at this time of year. So in terms of real-world authenticity, this site falls short. But there is a different kind of authenticity which comes from generations of pilgrims venerating a site. Let us call this imagined authenticity. In these terms, the Nativity Grotto is as authentic as they come. Pilgrims have been coming to pray at this cave since the third century (at least).
So where does the idea of a nativity cave come from? Two second century Christian texts - Justin's Dialogue with Trypho and the Protoevangelium of James - describe the birth of Jesus in a cave. We don't know where Justin's information comes from, but the fact that he mentions the cave is significant. In his Dialogue (78.5), Justin is very bothered by the fact that Trypho the Jew regards Jesus as yet another magician belonging to one the many mystery cults prevalent in the Roman Empire. The idea of a nativity cave is a big problem for Justin because it is very similar to the underground caves used for Mithraic initiation rites. So instead, Justin introduces the cave as a fulfillment of Hebrew Scripture. Isaiah 33:14 asks “Who among us can live with the devouring fire?" the answer to which is the righteous one, who is described as follows:
"he will live on the heights, his refuge will be the fortresses of rocks"
הוּא מְרוֹמִים יִשְׁכֹּן, מְצָדוֹת סְלָעִים מִשְׂגַּבּוֹ
Fortunately for Justin, the Septuagint alters the words of this verse to read, "he shall dwell in the lofty cave of the strong rock."
οὗτος οἰκήσει ἐν ὑψηλῷ σπηλαίῳ πέτρας ἰσχυρᾶς
The use of the word "cave" (spelaion) here provides Justin with the perfect defense against the charge of Mithraism. Jesus was born in a cave not because his parents were followers of a secretive underground mystery cult, but because he is the righteous one who "can live with the everlasting burning". Justin is thus the earliest author to write about the birth of Jesus in a cave, but he does not tell us anything about the cave's appearance in his own day.
The first author to describe the veneration of a specific cave in Bethlehem is none other than Origen, who writes:
With respect to the birth of Jesus in Bethlehem, if any one desires to have additional evidence from other sources, besides the prophecy of Micah and besides the history recorded in the gospels by the disciples of Jesus, he may observe that, in agreement with the narrative in the gospel regarding his birth, there is shown at Bethlehem the cave where he was born, and the manger in the cave where he was wrapped in swaddling clothes. What is shown there is famous in these parts even among people alien to true faith because it was in this cave that Jesus who is worshiped and admired by Christians was born. (Contra Celsum 1.51)
Origen's testimony is striking because it seems that he has actually seen the cave that he describes. Origen spent the second half of his life (231-254) in Caesarea Maritima, the capital of Roman Palestine. In his writings he alludes several times to visiting biblical sites, each time using the phrase "it is pointed out" (δείκνυται). This seems to be Origen's way of reassuring the reader that he was given a guided tour of the place in question, so his knowledge is reliable. Very few Christians engaged in pilgrimage to the Holy Land in the 3rd century. For the most part, the institution of pilgrimage only took off after the imperialization of Christianity in the mid-4th century. The Pilgrim of Bordeaux (333) is generally regarded as the earliest Christian to visit biblical sites in Palestine and write a travelogue, known as the Itinerarium Burdigalense. But at some point in the early third century Origen toured the holy land in search of places found in the Bible. What is so interesting is that he refers to the physical place here as "another source," as though it is comparable to the textual accounts found in the Old and New Testaments. This textualization of the land reminds me very much of the idea expressed in the title of J.M.P. Otts 1893 book, The Fifth Gospel: The Land where Jesus Lived. Of course, Origen does not mention anything about the date of Jesus' birth. The complicated question of how the Church settled on December 25 as the birth date is explored here.