Would NFTs on L2 cause token duplication since minting can technically occur on either chains?

I have recently thought about having NFTs which can be minted along the way. That is, when I produce a new artwork, I mint that artwork with a new ID on my token contract. So all tokens aren’t predetermined and are minted along the way.

I’m deploying my token contract on both Ethereum and Polygon so that I can mint on either one of the network and bridge between the networks too.

However, something come to my mind when I deploy to Polygon. What happens if I accidentally minted the same token ID on both the networks? Wouldn’t this be in issue of duplication? How am I going to know which one is the real one or which one came first?

Do all NFTs having an L2 sidechain have this problem too since the minting can technically happen on either chains? How is this usually resolved especially for the kind of NFT I’m trying to build?