One day, a huge rock crashed into Earth, somehow resisting all efforts to shoot it down as if it were protected by some mysterious force. Its impact into the African continent wiped out a substantial fraction of the Earth's population, and most of its infrastructure, while leaving the rock buried deep in the Earth's crust.
In the aftermath, while casualties mount up from secondary causes of death, some survivors begin to have violent migraines, some cases of which turn out to be fatal. However, those who manage to survive the migraines realize that they have developed psychic powers, the most common of which is telekinesis. There is no obvious factor which determines how strong or weak one's psychic power is, or why some people develop powers while others don't. It soon becomes evident that the psychics (the Awakened) are a minority, albeit a powerful one.
After some time, some Awakened realize that proximity to the crash site boosts their powers (in extreme cases, users are able to lift entire houses with little mental effort), and Awakened with telepathic skills begin to summon other Awakened to join them in their new Mecca.
EDIT FOR CLARIFICATION: With just their powers and nothing else, is it possible that the Awakened will be able to rebuild some semblance of civilization as we currently know it? For instance, can they erect buildings, and what would these look like?
The following limitations should apply:
- The Awakened population is necessarily small, at most a few hundred.
- Most of them are telekinetics, a handful are telepathic. I can allow for other psychic abilities if deemed necessary.
- The strongest Awakened can lift skyscrapers easily, or multiple smaller objects. Most can lift cars or huge boulders as long as they remain near the rock. Being able to lift more than their own body weight gives them the ability to self-levitate/ fly.