I don't think there's any way to count years without rooting it somewhere arbitrary. We cannot calculate the age of the planet, the sun, or the universe to the accuracy of a year (much less a second or nanosecond). We cannot define what "modern man" is to a meaningful level of accuracy, either, or pin down the age of historical artifacts.

Most computers use a system called "epoch time" or "UNIX time", which counts the seconds from January 1, 1970. Converting this into a human-friendly date representation is surprisingly non-trivial, since the human timekeeping systems in common use are messy and not rooted in hard math or in the scientific definition of a second, which was only standardized in 1967.

Tom Scott has an amusing video about this: https://www.youtube.com/watch?v=-5wpm-gesOY

There is also International Atomic Time, which, like Unix Time, counts seconds from an arbitrary date that aligns with the Gregorian calendar. Atomic Time is rooted at the beginning of 1958.

ISO 8601 also aligns with the Gregorian calendar, but only as far back as 1582. The official standard does not allow expressing dates before that without explicit agreement of definitions by both parties. Go figure.

The core problem here is that a year, as defined by Earth's revolution around the sun, is not consistent across broad time periods. The length of a day changes, as well. Humans all around the world have traditionally tracked time by looking at the sun and the moon, which simply do not give us the precision and consistency we need over long time periods. So it's really difficult to make a system that is simple, logical, and also aligns with everyday usage going back centuries. And I don't think it is possible to find any zero point that is truly meaningful and independent of wishy-washy human culture.