I kind of like the idea that the characters might be the first or second generation of supers, but that is not a necessity.
As a possible background that incorporates stuff brought up in this thread (for brainstorming; everything is still open):
In the nights from December 28th, 2000 to January 3rd, 2001, a large, fiery trail was seen in the night sky over the world. Quickly dubbed the Millennium Comet, this phenomenon was the harbinger of stranger events, as people developed strange powers, or changed their form altogether. Some rumors even spoke of otherworldly creatures roaming the cities. These were the world's first brushes with the abilities of superheroes and supervillains.
Ever since these days, superheroes and villains have become more common, and most could be linked somehow to the appearance of the comet - but not all. As time passed, the UN announced the creation of a large team of such superheroes. This step, originally viewed with suspicion by both normal humans and supers, proved to be an important one in restoring the world to some order after the chaos the rise of supers brought.
Scientists observing the - to this date unknown - Millennium Comet found that it could not possibly exist, as the calculations of its orbit showed that it must have moved through the sun about twenty years ago. Further observations suggested that its orbit would change, creating a 30-year long cycle in which the Comet would come close to earth again. Only time will tell if this orbit will be stable... and only time will tell if the return of the comet again portents a rise in supers.
Eh, I'm sure you all can do better than I.
