The trouble is, there are quite a lot of visiting relatives. The place is packed out. And most of their homes are small, maybe only a couple of rooms, including a general purpose room that allowed some space (at a lower level) for animals to be kept inside at night (hence the feeding trough).
Wherever it was that Joseph and Mary stayed, the guest room was already taken. They would have camped (with some others probably) on the floor of the main room. They arrived in Bethlehem some time before the birth (people in those days also knew how long it takes to have a baby, and whether it is a good idea to travel long distances if the birth was imminent).
So they are guests in the home of a relative who has also probably been hospitable to others at the same time. And the baby is born – on the floor I suppose. And to keep the baby out of the way of the rest of the household he is laid in the feeding trough that would have been against the wall at the end of the lower portion of the room.
Is it difficult to imagine a crowded house, full of excitement at the birth of a baby? Not difficult at all. How many visitors would they have had? Every relative many times removed would have dropped by to see the baby, although we are only told (for special reasons) about two groups, who were probably not relatives.
It is very human, very family, very ordinary.
Dale