I’m totally out of my depth here and this is just my curiosity but going by the Wikipedia article, “American spelling” is a standardisation started by Webster. Regardless of the spellings chosen, it dates no earlier than 1825.

Webster hoped to standardize American speech, since Americans in different parts of the country used different languages. They also spelled, pronounced, and used English words differently.

Of course I’ve no idea how old “British spelling” would be with similar reasoning but I guess we also had variations in spelling that got standardised at some point?