Hi CS,
Well, that depends on whether the calendar that we now use was actually set to have begun in the year of Jesus' birth. The gregorian calendar that is now in use didn't come into being until the 1500's. A man by the name of Dionysius Exiguus chose the starting year of the calendar by his reckoning of when Jesus was born. However, he chose this date based on Luke's account that Jesus was 'about' 30 years old shortly after the 15th year of the reign of Tiberius Caesar. Matthew's gospel tells us that Jesus was born while Herod the great reigned. It is believed that Herod the Great died in 4BC so, if this is correct, then Jesus had to be born 4BC or earlier.
So, the truth is that we don't any of us know when Jesus was born as far as an exact day or year. The best we can do is approximate it sometime within a 5-6 year time span. BTW, there is no year 0. The first year of any calendar is the 'first' year.
Keep in mind that in Jesus' day years weren't counted as we count them today. Time was established as being the 'year of so-and-so's reign. This is important because we can't today establish with any certainty that Herod's death occurred in the year that we account as 4 BC. Here's a study that shows some of the difficulty in our ability to establish such dates:
Did Herod the "Great" Really Die In 4 B.C.?
When one begins to understand what is required for modern day calendars to give dates in the days before and during the life of Jesus, there are loads of assumptions that are found to be taken.
God bless you.
In Christ, Ted