I mean, zeroth would still be zeroth; it's just based on the cardinal the moment before it arrived rather than after, assuming you start with nothing and add objects. Unfortunately that's not conventional, probably in any language, and so you get a situation where a positional notation clashes with how we want to talk about the larger divisions of it casually. This sort of thing is exactly why computer science does use zero indexing.

Relatedly, there was also no year 0; it goes straight from 1 BC to 1 AD.