There's no real historical evidence of Jesus. And the new testament doesn't lend itself to naming a date very well because it's contradictory. It says that Herod was the governor of palestine during the time and that he administered the first census of the province (a census which, apparently, had a bizarre provision that you go back to the pace of birth of your ancestors - a provision that was apparently never recorded in any historical documents). Pilates died in 4 BC and the first Palestinian census happened around 6 AD.
You are wrong on all accounts- The more likely date of Jesus birth is September...still there is plenty of historical evidence for his existence.
. When was Jesus born?
A. Popular myth puts his birth on December 25th in the year 1 C.E.
B. The New Testament gives no date or year for Jesus’ birth. The earliest gospel – St. Mark’s, written about 65 CE – begins with the baptism of an adult Jesus. This suggests that the earliest Christians lacked interest in or knowledge of Jesus’ birthdate.
C. The year of Jesus birth was determined by Dionysius Exiguus, a Scythian monk, “abbot of a Roman monastery. His calculation went as follows:
a. In the Roman, pre-Christian era, years were counted from ab urbe condita (“the founding of the City” [Rome]). Thus 1 AUC signifies the year Rome was founded, 5 AUC signifies the 5th year of Rome’s reign, etc.
b. Dionysius received a tradition that the Roman emperor Augustus reigned 43 years, and was followed by the emperor Tiberius.
c. Luke 3:1,23 indicates that when Jesus turned 30 years old, it was the 15th year of Tiberius reign.
d. If Jesus was 30 years old in Tiberius’ reign, then he lived 15 years under Augustus (placing Jesus birth in Augustus’ 28th year of reign).
e. Augustus took power in 727 AUC. Therefore, Dionysius put Jesus birth in 754 AUC.
f. However, Luke 1:5 places Jesus’ birth in the days of Herod, and Herod died in 750 AUC – four years before the year in which Dionysius places Jesus birth.
D. Joseph A. Fitzmyer – Professor Emeritus of Biblical Studies at the Catholic University of America, member of the Pontifical Biblical Commission, and former president of the Catholic Biblical Association – writing in the Catholic Church’s official commentary on the New Testament[1], writes about the date of Jesus’ birth, “Though the year [of Jesus birth is not reckoned with certainty, the birth did not occur in AD 1. The Christian era, supposed to have its starting point in the year of Jesus birth, is based on a miscalculation introduced ca. 533 by Dionysius Exiguus.”
E. The DePascha Computus, an anonymous document believed to have been written in North Africa around 243 CE, placed Jesus birth on March 28. Clement, a bishop of Alexandria (d. ca. 215 CE), thought Jesus was born on November 18. Based on historical records, Fitzmyer guesses that Jesus birth occurred on September 11, 3 BCE.
