Zero was a big case for the Ancient Greeks also.
A not-so-clear one, in a way.
They used it in a strictly defined way; to show, for example, where there is a gap in some numerical representation. For example, like when we write 1506. Here '0' serves us as a 'place holder', which reveals exactly the special use of '0', because here '0' essentially tells us that there is an empty place between the number '5' and the number '6', thus making the difference between '1506' and '156'.
They also used it in Astronomy, but generally, zero wasn't ...a given. There was discussion about it, also in another level; if it means "nothing", if we can say that nothing is something, e.tc.
In the Greek language though, the word for zero is μηδέν. And its etymology is "not even one thing". Something like that...
So, zero is a long story,but to me, zero is not an empty vessel.
When it comes to the way we count years, well, you are right that there is a case. It is a topic that I think raised various questions and discussions when we were reaching the year 2000.
I enjoyed the piece!