Faster than light travel is a theory fraught with all sorts of intractable problems, Star Trek notwithstanding. The bottom line is it would take over 30,000 years to get to the nearest star at the current top speed that we’re capable of.
“Unlike the article, we are not talking about interstellar space travel. We’re now talking about establishing habitats within the Solar System. Asteroidal habitats can house several times the current population of the Earth. Such communities and their habitats can potentially survive long after he Earth is made uninhabitable by the Sun or consumed by the Sun after the Sun has grown large as a Red Giant star.
Any space faring human societies which have mastered the ability to make asteroids into their homes may if they so wish ever so gradually propel their asteroid out of the Solar System on interstellar voyages lasting lifetimes. The technologies required to propel the asteroids on their interstellar voyages can use the ion rocket engines first patented by Robert Goddard before the Second World War. No “warp drives” or “stargates” are required to be invented. Only time is required in the form of multiple lifetimes and multiple generations. Of course, the less adventurous can simply “stay home” and watch the extinction of life on the Earth from nearby in he Solar System.