Several Biblical approaches for an approximate date, assuming that there was a 'real' Jesus - and I believe there was. Consider the 'course' of John the Baptist's priesthood give us the month he served at the temple and had his vision. That would take us to an October date for Jesus' birth.
The shepherds in the field at night would take us to a similar date, and that removes a December birth.
Also, December 25 is the date for the rebirth of the sun, making it an unlikely date for the birth of God's son.