But that was a trailer. I didn't say TWOK was the first thing that ever proposed the idea in any context, simply that it was the first production to state canonically what the century was.
But then in the same film you had Khan stating that he was a prince on Earth "200 hundred years ago".
Also remember McCoy grings Kirk some Romulan Ale dated 2283. Since it "takes this stuff a while to ferment," it would be closer to the end of the century. Even if they were being sarcastic about the vintage, it's at least 2283.
Unless someone wants to say the label was a typo.