>Yeah, you should avoid needing that but it is certainly not impossible given high enough tech level & in-space infrastructure. Launch loops and orbital elevators should have more than enough capacity to enable that.
I think you're underestimating the effort, resources and logistics something like this would require.
In 2016, there were ~256 live births per minute[0]. That works out to ~369,000/day.
Even multiple space elevators couldn't hope to come anywhere close to that, but perhaps with launch loops as well we might be able to approach that.
But even if we could, how much of global production of, well everything, would need to be dedicated to getting even 350,000 people and the stuff they need off the earth every single day?
>Much bigger problem actually is where to put those billions once you have to move them in a hurry off a planet.
An excellent point. Even if you didn't need to hurry, the resources required just to stage such a migration are staggering and would likely exceed the production capabilities of the planet.
But as you point out, we don't really have any place to send all those "colonists" so the point is moot.
[0] https://en.wikipedia.org/wiki/Birth_rate