The Gospel writers either did not know when the event happened or they did not feel the information was important enough to pass along. We can only speculate. Some speculate that the church associated the birth of Jesus with the winter solstice and assume that the church chose December 25 as a matter of syncretism with Hanukkah, Kislev 25 in the Jewish calendar.
In the Gospels, John comes in the role and spirit of Elijah. Jewish tradition maintains that Elijah will appear at Passover to announce the coming of the Messiah. For that reason, Jewish homes set a place at the Passover Seder table for Elijah. If John was “the Elijah who is to come” (Matthew 11:14), it isn’t reasonable that his birth took place at Passover. If John was born on Passover, then it is reasonable that Jesus should have been born six months later at the onset of the Feast of Tabernacles/Sukkot. Luke 1:36- And behold, even your relative Elizabeth has also conceived a son in her old age; and she who was called barren is now in her sixth month”.
Additionally, traveling to Bethlehem at instruction from Herod, the wise men found a child and his parents in a house, (Matt. 2.11); whereas, in the Luke account the shepherds found Him in a stable (Luke 2.7,16). There is no discrepancy between these two accounts, for likely the new mother and child were moved from the stable following the birth. The fact that he was born in a stable is a clue to the time of his birth, for in Hebrew a stable is called a “sukkah” (Genesis 33.17). “Sukkot,” the name of the festival, is the plural form of this word. It is even significant that they had to seek shelter in the stable, “sukkah” due to “no room in the inn” (Luke 2.7). It was only during the 3 pilgrim festivals (Passover, Sukkot and Shavuot) that Bethlehem would overflow with people.
In ancient times, reporting for a census would be done over a several month period due to the difficulties of travel, as well as the economics of an agricultural society. It is highly improbable that so many people would be in Bethlehem for Caesar’s census all at one time.
As stated above, Joseph and Miriam (Mary) bring the child into Jerusalem forty days after Yeshua’s birth. This indicates that Herod died within this same forty days. The chronology of these forty days is imperative in correctly finding His birth date. The probable scenario is this: Joseph and Miriam (Mary) come to Jerusalem for the festival of Sukkot (September or October), planning to stay in the nearby Bethlehem in order to register for the census. Unable to find a room at the Inn due to overcrowding for the pilgrimage, they are given shelter in a Sukkah, or stable. During the night the wise men arrive in Jerusalem and speak to Herod. Meanwhile, Miriam gives birth. They go to pay homage in the sukkah, while the wise men are making their way to Bethlehem. The wise men arrive and during the night are warned by G-d concerning Herod. Joseph and Miriam take the child and flee to Egypt and remain there until they are told by G-d that Herod is dead. On returning to Judea, they circumcize Yeshua according to the Law on the 8th day.
It is apparent that as long as Herod was alive, they could not appear at the Temple. Therefore, if the approximate date of Herod’s death could be determined, it would establish the season of Jesus’ birth. The Jewish historian, Josephus, who lived during the first century C.E., documents in detail Herod’s death.
Josephus relates that Herod became very ill immediately following an act of impiety against the priesthood, at which time an eclipse of the moon occurred. This eclipse, the only one mentioned by Josephus, happened March 13 in the year of the Julian period 4710, and the fourth year before the Common Era. Herod’s illness lasted several months and is documented in great detail as being painful and distressful. Many times cures were sought and brought about temporary relief; however, nothing prevented imminent death. According to Josephus’ calculations, Herod’s death occurred about September, in the fourth year before the Common Era. Therefore, with the knowledge that Herod died in autumn, the same time of year as Sukkot, and that his death was within forty days of the birth of Yeshua, it is convincing that Jesus was born at this time of year.