While they were there, the time came for her to give birth. She gave birth to a son, her firstborn. She wrapped him in a blanket and laid him in a manger, because there was no room in the inn. Luke 2:6-7 (from The Message Bible)

Whenever I get to this part of the story, I can never quite believe that Mary and Joseph traveled to the city of their ancestors and there was no one in the little village who would take them in. Also, being as Bethlehem was a little village, did they really have any inns, anyway? It wasn’t like Bethlehem was just off the interstate and there was a Super 8 to cater to the camel drivers. The word here, inn, would be better translated to inner room.
Joseph and Mary probably found some relatives who would give them lodging, but they already had house guests sleeping in their inner room, or guest room. The only space left for company was the stable, which wasn’t a cave out back, as usually depicted. Homes at the time more often had the area for the animals in the same building. It made more sense that way, the animals would be kept safe and they would throw off body heat to warm the house in the cold of night.
Yes, Jesus was probably placed in the manger - what a perfect crib that would make, don‘t you think? But I picture that Mary was surrounded by female relatives along with the cattle and donkeys.
Why do we always see Mary and Joseph in this cave by themselves with the baby Jesus and the farm animals? Because Jesus was born in the most humble of places, as foretold in scripture, and from these humble beginnings he would become king. But at that time, you had to be born in a palace to ever become a king. So whether he was born in a cave, or in the stable within the home of a common, working class family, he would never be able to rise to a position of ruling a kingdom. Of course, they did not realize at the time what it really meant to rule the kingdom, to rule the world.

If you have children, were they born in a clean bright hospital? Can you imagine giving birth any place else? Your bathroom floor? The back seat of a car? A barn? The women of the Bible never gave birth somewhere sterile. There was no such place back then.