When is earliest mention of the Church tradition that Jesus was born in a cave? The birth of Jesus as recounted by Luke says that:


  7 And she gave birth to her first-born son and wrapped him in swaddling cloths, and laid him in a manger, because there was no place
  for them in the inn. Cf. Luke 2:7.


How did it come to be known in Church Tradition that Jesus was born in a cave, and when is earliest mention of this tradition?
The earliest reference I can find is Justin Martyr (c. 100 – 165 AD) who wrote in Dialog With 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. (1)