The year isn't actually exactly 4000BCE. There are a number of exact dates used, based on counting backwards years of historical figures in the bible. There are several such dates, mostly varying based on how certain passages as interpreted, which manuscripts of the bible are used (the numbers can vary between them), and when you transition from using biblical chronology to historically dateable events (the usual biblical dating has too few years between the destruction of the 1st Temple and things after, particularly Alexander's conquest, which is a common dating reference point in the region)

One such date is the Hebrew calendars, which places the epoch at 3761BCE. This is from a calculation in Seder Olam Rabbah, a 2nd century text. Before then it doesn't seem anyone systematically added up the years in the bible to calculate the supposed date of creation. There are a wide variety of dates calculated by Christians from the 2nd century on, most of which but the date of creation substantially earlier, at least 5000BCE.