>>213521562people didnt really track years in the BC/AD sense up until around 800 AD in most of europe.
romans tracked it by name of the consul that was in office at that time.
when central roman authority in europe slowly collapsed, migrating people brought their own calendars with them, but still pretty much all of them worked with the familiar lunar 12 month cycle.
byzantines at first had the roman-type calendar that started with the founding of rome in 753 BC. later they adopted a more christian calendar that started with the hypothetical founding of the world around 5000 BC.
in western europe an AD/BC calendar only started to emerge in around 800 AD with charlemagne and the franks, when the church established worldly authority and central governments were interested and capable again to keep good records.
calendar tracking and maintenance has been a huge topic in several church councils over the centuries, and jesus birth is just an approximation anyways because he's never mentioned in any historic documents outside of the bible. its just an educated guess that everyone ran with.