I don't think the amount of "unexplored" or "undeveloped" land is a good metric for social mobility. Economic growth is. New "frontiers" are created all the time. They do not have to be in the physical world (e.g. computers, the web, biotech, the App store, social media influencer, crypto, and now AI). Even in the physical world, frontiers can sometimes expand. Desirable land can be created in the middle of a desert (e.g. Las Vegas), we just don't want to anymore.
Despite its many flaws, I think the US is still better than pretty much anywhere else in the world.