No one knows for sure the date of John the Baptist’s date of birth because the Bible does not tell us, but if pushed my first choice would be 31 March 3BC.
Why 31 March 3BC? Because it fits nicely into rhythm and timing of the Gospel story even though it goes against other more tradition dates.
The Jews believed that the ‘Elijah’ was to appear at the time of Passover to announce the arrival of the Messiah. It would be fitting that John would fit into the perfect timing and divine hand of the of the Gospel narrative and be born at Passover.
Timing of Zechariah’s Service at the Temple
Zechariah belonged to the priestly division of Abijah. One for the weeks of service of this division is the week before Shavout (Pentecost). If we assume Elizabeth conceived shortly after Pentecost John would have been born around the time of Passover.
Mary stayed with Elizabeth for three months to help her during the final trimester of her pregnancy. It was now the time of Passover (Pesach) in 3BC when Elizabeth reached full term and she gave birth to a son. When her neighbours and relatives heard the news they praised the Lord for his great mercy and they shared in Elizabeth’s joy. TJB 1:29
3. Timing of the start of John’s Ministry
John started his ministry in 28AD in the 15th year of Tiberius Caesar (which was in 14AD) which is fits perfectly which is when John would have turned 30 years of age. This fits nicely for this is also the age that men were old enough to start their ministry in the temple.