So far we have sent a few humans, who mostly have just landed on the shores of the continent (LEO). A few have ventured further inland (to the Moon). And that's it.
We also have many spacecraft that have flown over the continent. And a few have landed on other planets. But we really don't know too much about it. Despite excellent images from orbit, we don't have much ground truth.
But like Antarctica and more so - we do know it is incredibly hostile to human life.
So for us to colonize space right now is a bit like the early C 20 explorers setting out in a colony ship to colonize Antarctica.
Whether we will do it some day, whether it is even worth doing, and whether it is a good idea I don't know.
But first we need to explore more. Which may involve temporary settlements like the ones in Antarctica, but not colonization.
Maybe as we do this, we find ways that humans can survive long term in space in conditions not that different from Earth - even perhaps easier than many places on Earth. There are ideas that might work here - such as the Stanford Torus - I think myself more likely to work than settlement on a planetary or luanr surface because it is more controlled - you can set the day night cycle, temperature, atmospheric pressure - levels of gravity even - in a mini world which can mimic anything, e.g. tropics or whatever.
The analogy with America is flawed - as the US was a hospitable place warm, easy to grow food, abundant natural vegetation and wildlife - which already had indigenous humans there - who were also doing just fine without the colonizers.
And we have never, ever, tried to colonize anywhere where humans can't breath and can't go out of doors without oxygen and spacesuits, and with no soil to grow things, and no native vegetation - and need to build greenhouses to cover the land to grow things, and those greenhouses needing to be engineered to withstand tons outward pressure per square meter - and buildings built like tanks and covered in meters of cosmic radiation shielding.
So - if we do ever do it (and I'm not entirely sure myself if we would, or should actually) - then it surely won't be by just sending a bunch of would be colonists in a few habitats and hoping that somehow they will become a seed of a new colony. So - SpaceX and Mars One's plans - I think just don't have a clear enough "big picture" - Stanford Torus was far better thought out - but it would need more research and you need a new reason for building the Torus as I doubt if you need 10,000 people in space to build solar power satellites with modern technology.