Now the Scripture speaks, respecting the place of the Saviour's birth— that the Ruler was to come forth from Bethlehem— in the following manner: “And you Bethlehem, house of Ephrata, are not the least among the thousands of Judah: for out of you shall He come forth unto Me who is to be Ruler in Israel; and His goings forth have been of old, from everlasting.” Now this prophecy could not suit any one of those who, as Celsus' Jew says, were fanatics and mob-leaders, and who gave out that they had come from heaven, unless it were clearly shown that He had been born in Bethlehem, or, as another might say, had come forth from Bethlehem to be the leader of the people.
With respect to the birth of Jesus in Bethlehem, if any one desires, after the prophecy of Micah and after the history recorded in the Gospels by the disciples of Jesus, to have additional evidence from other sources, let him know that, in conformity 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. And this sight is greatly talked of in surrounding places, even among the enemies of the faith, it being said that in this cave was born that Jesus who is worshipped and reverenced by the Christians. Moreover, I am of opinion that, before the advent of Christ, the chief priests and scribes of the people, on account of the distinctness and clearness of this prophecy, taught that in Bethlehem the Christ was to be born.
And this opinion had prevailed also extensively among the Jews; for which reason it is related that Herod, on inquiring at the chief priests and scribes of the people, heard from them that the Christ was to be born in Bethlehem of Judea, “whence David was.” It is stated also in the Gospel according to John, that the Jews declared that the Christ was to be born in Bethlehem, “whence David was.” But after our Lord's coming, those who busied themselves with overthrowing the belief that the place of His birth had been the subject of prophecy from the beginning, withheld such teaching from the people; acting in a similar manner to those individuals who won over those soldiers of the guard stationed around the tomb who had seen Him arise from the dead, and who instructed these eye-witnesses to report as follows: “Say that His disciples, while we slept, came and stole Him away.
And if this come to the governor's ears, we shall persuade him, and secure you.”
Source: Against Celsus (New Advent)