In the Dialogue with Trypho, chpt. 70, Justin quotes Isaiah 33:13-19:

The man who walks in righteousness, speaks in the right way, hates sin and unrighteousness, and keeps his hands pure from bribes, stops the ears from hearing the unjust judgment of blood closes the eyes from seeing unrighteousness: he shall dwell in the lofty cave of the strong rock.

Then in chpt. 78 he makes the claim that Christ was this man of righteousness and that he was born in a cave:

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, and here the Magi who came from Arabia found Him.