Zacharias served as a high priest and based on his tribe, we know when he served John would have been born on Pesach. Most Jews believed that Elijah would come at Factor in when Miriam visited her cousin Nine months back from Sukkot is Chanukah where the light entered the temple. Yah'shua's birth on Sukkot is supported by Elizabeth's pregnancy of John the Immerser.
shalom b'shem Yah'shua
The time sequence is outlined by the Holy Word of Elohim in Luke 1 with Zacharias.
and when he was struck dumb and when John was conceived.
Pesach to announce the coming of the Messiah
Elizabeth, timing of Yah'shua's birth can be ascertained.
by this reckoning, the Anuniciation would have come about this time. Could be that the Christian calandar we have might have come about as the Church sought to disaccosociate herself from the Jewish calendar, to brinbg herhelf in line with the Roman calendar.