Well, technically, rigorously defined counting starts at 0, not at 1.
You can define counting as defining an injective function from your set to the natural numbers, and then you need to have some element going to 0 - as per the definition of a countable set[0].
Also, both the cardinal[1] and the ordinal[2] numbers are defined as starting from 0, just like the cardinal numbers.
"Countable" is not the same as the "countable numbers" nor is it the same as the process of "counting".
The process of counting might be defined as what starts to happen when you stick up one finger and say something to emphasise what that finger means. That something will not be zero. Ever.
When you count your sheep into your pen, you will of course start: "Yan, tan, tither, toe" Trust me that yan does not mean zero.
Also note that if you search those terms, you will get a valid result and conclude I've misspelt some of those Cumbric words. I haven't, according to living relos of mine. Speling is a bit odd anyway when you go back a few centuries and I'll wager that tither is more likely than tethera because it is very slightly more easy to say. Tethera is three syllables but tether is two, bordering on one. However tethera could be pronounced "tethra", ie drop the extra e when spoken.
The counting numbers are fairly rigorously defined and are the numbers we use when we don't have access to more than the usual four dimensions, imaginary thingies, quaternions, etc etc.
> You can define counting as defining an injective function from your set to the natural numbers, and then you need to have some element going to 0 - as per the definition of a countable set[0].
You can define counting as an injection into other (equivalent) sets just as rigorously.
Given that a counting always starts at one, because that is what defines counting, then there cannot be a zeroth prime.