I know that the definition of "claimed land" might be a bit fuzzy but approximately, when was all "useful" land (e.g. excluding Antarctica) on Earth claimed by countries?

I'm going to go ahead and be the pedant, I'm afraid. It's hard to imagine, but Polynesians were still colonizing the last uninhabited Pacific islands under a thousand years ago. And by that time, as you know, there were already many entrenched and competing ideas of what land ownership meant (if anything) across the globe. So you have to settle on someone's idea of "claimed land" rather than trying to maintain a neutral, agnostic position to what is by definition an arbitrary concept.

You might as well tailor the question towards the Western viewpoint given our obsession with neat and tidy (and imaginary) boundaries, anyway.