No one knows for sure when Jesus was born. We're only told Mary conceived 6 mos after Elizabeth. (John the Baptists mother.)
There is strong speculation to the timing based on Zechariah (Elizabeth's husband).
It was his turn to serve in the Temple as he was a priest of Abijah in June. Angel Gabriel visited Zechariah telling him his wife would conceive. 6 months later Gabriel visited Mary.
Its possible Jesus was born in September.
More about it here:
https://www.gotquestions.org/was-Jesus-born-in-September.html