How do you move 8 billion people to another planet when it costs a $billion to send just 5 people into Earth orbit? Worse, there's nowhere enough sunlight and water anywhere in this solar system to sustain more than a handful of people.
No, if mankind can't make it here, we can't make it anywhere.
These are gradual things that unfold over decades to centuries.
But I'm extremely doubtful we would ever reach a point where moving everyone off of earth is easier than fixing whatever is broken with earth. Or that it would even get within a factor of 10.
On the other hand, getting to 1st cosmic speed takes a lot of energy released in a relatively short burst or some kind of space elevator which we cannot build yet.
You cannot make this "gradual" really. You either get to orbit or don't. The "gradual" phase of getting into space is done. We got to orbit.
We need a major economy and scale breakthrough now or you cannot even try sending people off anywhere. So major that small improvements as done by SpaceX will not get there in centuries.
All the more reason to develop your space program.
At the risk of pointing to Movies, but yet, one of the underlying themes in the movie Interstellar is some day there will be no option but to leave.
So its about time we think seriously about mining asteroids, space colonies and having some kind of permanent self sustaining and growing colonies in space.
Sure Humans are still likely to have the same problems, but you have eliminated the biggest threat to our existence, and we now have thousands of years at our disposal to plan the next steps.