Both the source I linked to and Wikipedia have material on the "missing years." They're very well known.
The nub of the argument is the Persian period. According to secular historians this lasted over a hundred years. According to traditional Jewish chronology, the period of Persian rule, between the Persian conquest of Babylonia and Alexander's conquest of Persia, was a mere fifty-two years and presided over by four kings. I'm sure the reference I linked can tell you far more than I ever could.
As to when Jewish chronology begins, traditionally it is from when Adam first spoke after his creation on the Sixth Day. But there is some dispute as to whether the year 1 refers to the year that began with Adam's creation or the "year that never was" that occurred in the Mind of G-d, which would have made Adam's creation the start of the year 2. Also, if Adam died in the year 930 at the age of 930, then the year that began with his creation would have been the year Zero (otherwise he would have been only 929 or 928 years old). There is a dispute about the year of the Roman destruction as well, whether the traditional date refers to the year it occurred or the first year afterward.
Lots of places on the Internet could give you much better information than I. Maybe even some of the Jewish FReepers.
So it did start w/Adam. Thanks!
“Maybe even some of the Jewish FReepers.”
I assumed you were Jewish. Am I incorrect in that assumption?