A year zero does not exist in the Anno Domini (AD) calendar year system commonly used to number years in the Gregorian calendar (nor in its predecessor, the Julian calendar); in this system, the year 1 BC is followed directly by year AD 1. ... And there is a year zero in most Buddhist and Hindu calendars.
Did the year start with 1?
Has the year always started on 1 January? In some ways, yes. When Julius Caesar introduced his calendar in 45 B.C.E., he made 1 January the start of the year, and it was always the date on which the Solar Number and the Golden Number were incremented.
Was the first year year or year 0?
Well, actually there is no year 0; the calendar goes straight from 1 BC to 1 AD, complicating the process of calculating years. Most scholars believe that Jesus was born between 6 and 4 BC (Before Christ) and that he died between 30 and 36 AD (Anno Domini, latin for "in the year of the lord").