“While they were there,
The time came
Ἐγένετο δὲ ἐν τῷ εἶναι αὐτοὺς ἐκεῖ ἐπλήσθησαν αἱ ἡμέραι τοῦ τεκεῖν αὐτήν,
Luke had a very simple statement, just like Matthew, chapter 2:1, about the birth of Jesus. While they were there (Ἐγένετο δὲ ἐν τῷ εἶναι αὐτοὺς ἐκεῖ) in Bethlehem, the time came for her to deliver her child (ἐπλήσθησαν αἱ ἡμέραι τοῦ τεκεῖν αὐτήν). Her pregnancy had reached its end. After all that had preceded, the main event had arrived. As any mother, Mary was excited about the birth of her child. Joseph might also have been concerned.