Growing up, I learned that the current calendar we use has catholic origins and I found it interesting and somewhat ironic that we count the years from the birth of christ, whose existence is atmost debatable(?), especially when talking about history. Is it just for commodity at this point or are there more historical events that define A.D. 1?
This answer from u/sunagainstgold describes the creation of the modern calendar system in the sixth century and its eventual adoption. https://www.reddit.com/r/AskHistorians/comments/5izv93/comment/dbc9y1r/
To your specific question as to whether the date of 1 corresponds to any known evidence for the birth of Jesus or if it was a guess, she addresses that in a comment in that thread:
"On the other hand, it's not actually known (a) how Dionysius calculated the incarnation of Christ or (b) whether his idea of "incarnation" meant the birth or the conception of Christ. So if he did make a math mistake, we honestly would have no way of knowing."
So it's probably best not to drive yourself too crazy trying to figure out how a sixth century monk may have approached the problem and arrived at the solution. He may have been trying to correlate it to the end of Herod the great (who's alive in the bible when Jesus is born and orders a massacre of innocents, something that isn't believed to have happened) in which case he may have missed by 4 years (but it's not like we know for 100% ourselves and only being off by 4 given the evidence available to him isn't too shabby - and we don't even know if he was or wasn't alive when Jesus is born, biblical story notwithstanding). I think that's the source of a myth that our calendar today is "missing" 4 years.
Edit: on the subject of Jesus, I think it's generally accepted that he existed (and was probably born 1-ish AD, give or take). There's no physical evidence of his existence...BUT there's no physical evidence for pretty much anybody 2000 years ago, much less a non-noble regular guy from what was a bit of a backwater kingdom. We have, for example, just one small inscription on a small stone that appears to refer to Pontius Pilate, a person who, in his life, was much wealthier and in a better position to leave earthly evidence.
When it comes to using the Bible as a historical source some people suggest a minimalist approach - assume it's fictional unless corroborated with other evidence (for example the Babylonian captivity is a well documented event where the king Nebuchadnezzar II sacked Jerusalem and deported a large number of its population across the neo-Babylonian empire. I'm no historian but that minimalist approach seems to effectively throw out the Bible as a useful historical source which seems a bit much. It was written by non-historians, often long after and far away from the events, who had an agenda with their writing and viewed and interpreted the events of the world through a specific lens.....but that's true of almost all the writing we use as historical sources.