If you want to look at it that way, then year 0 is when earth started orbiting the sun.

But that's a bit silly. Afterall, we don't usw Kelvin inszead of Celsius despite Celsius being "made up" and Kelvin measuring the actual null point.

The obvious meaning of someone saying "year 0 doesn't exist" is that the Gregorian calendar does not have a year 0; the year before 1 AD is 1 BC. It's not a math thing, it's a protocol thing.

Your point on consistency is just wrong. There is no reason that "believing years exist" would necessarily imply "believing all numbered years exist"