Luke sets the stage, “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” (Luke 2:7).
The last word, “inn,” is what usually fosters the narratives as described above. However, the English word is not a full translation of the Greek.
The word used in the original text is kataluma and is best understood as a “guest room,” not a type of commercial inn used for travelers. For that type of lodging Luke uses the word pandokheion. Additionally, Bethlehem was Joseph’s “hometown” and he likely had relatives to stay with.
Even more to the point, very few people would want to give birth in a type of public motel. Inns at that time did not have a good reputation and Mary would have wanted privacy for such an intimate event.
Furthermore, a close reading of the text reveals that Joseph and Mary had been in Bethlehem for a number of days before her birth.