Space travel and colonization is so far off from a realistic option that you might as well be talking about Captain Marvel swooping in and saving the planet. The physics simply don’t allow it to happen (short of some truly major breakthrough like warp drive/time travel). And we don’t have hundreds or thousands of years to wait for things like that — the current trends point to a few decades at best to solve these problems.
Also, colonization creates more people. The current ones stay where they are, while only a few adventurers move to the new place, and then have kids there. Most people are not going to give up a lifetime’s worth of building a life somewhere, at least not in the numbers needed to impact total population.
I don't know, that seems a bit pessimistic. Right now, space travel is a tiny fraction of global economic activity. What if that increased 10x, 100x, or 1,000x?
Submarines and self-contained vessels might be a good metaphor/approach, as compared to a full-blown colony. It doesn't seem implausible that we could have millions of self-contained spaceships, each carrying hundreds of people, within ~200 years, assuming that serious percentages of GDP are put toward it.
We could, but hundreds of millions is a small fraction of our population and 200 years is too long if it’s an important part of the solution.
Also, cislunar space is much easier than colonising the planets, which is in turn orders of magnitude easier than colonising other star systems — even if you can find enough people to do it, which is hard because why would Joe or Jane Average want to go to a deep space colony where ping-time is measured in years at best, or dozens of geological epochs at worst?
Also, colonization creates more people. The current ones stay where they are, while only a few adventurers move to the new place, and then have kids there. Most people are not going to give up a lifetime’s worth of building a life somewhere, at least not in the numbers needed to impact total population.