Justin Martyr (c.103-165 AD), wrote in Dialogue with the Jew Trypho:
But when the Child was born in Bethlehem, since Joseph could not find a lodging in that village, he took up his quarters in a certain cave near the village; and while they were there Mary brought forth the Christ and placed Him in a manger . . . (The Ante-Nicene Fathers Vol. I, p. 237).
The Church of the Nativity was built by Helena, Constantine’s mother in 339 AD. It was built above the traditional cave which is associated with Jesus’ birth. This photo shows the approach to the church.
Here is a close-up of the entrance to the church.
The above photo is a scanned slide I took in 1999.
Inside you can see the cave, the traditional place of Jesus’ birth.
Other early evidence pointing to this spot as the location of Jesus’ birth includes that of Origen and Jerome.
For some thoughts on the useful purpose of shrines in this context, see Ferrell Jenkin’s post here.
Click on images for larger view.