Let just say the if human kind don’t destroy themselves by wars and violent, diseases, and so on, there are others tons of ways human can be wiped out of the Earth from space. The most scariest ways of all is from a Neutron Star. It’s when, not if, when we have indication that a Neutron Star is heading toward Earth or our solar system, off course we could know, but we will not be able to stop or prevent it from coming. The Neutron Star is so far unstoppable, it is worst than than asteroids or any other moving objects in space. So when the Neutron star come we better run.
Run we will, and that is the reason we have space program such as NASA, international space station, and so on. However now, if we know we only have 100 years to prepare to survive to escape Earth, then we better get started. However as of today, the good news is, no Neutron Star heading toward earth or our solar system or even our galaxy yet. So let say we know when, then what? You guess it we can build one, but most likely need to speed up if we only have 100 years to prepare, it is not as easy as we may think. How many people can we get out of Earth by then, what will people reaction be during this time period? and so on and so forth.
You know with all the methodology have been discussed, at a high level look, I would look at the “how” in this way. Each continent or even each countries build a space elevator, I believe it is more cost effective than having explosive chemical rockets, then construct living space modules universal that can hook up to the spaceship easily. The spaceship will be connected assembled by each countries and let the countries leaders themselves determine who gets to go, off course all these will be based on standard quality process and off course exception process as well.