What if the aliens are the cause of superpowers? Their initial invasion force was clandestine, working in secret to subvert humanity via technologically advanced genetic engineering. They manufactured a virus that worked on a subset of humans and granted them superhuman speed, agility, and strength while degenerating their minds to a nearly feral, animalistic state. Humans are attacked by these new creatures, investigate, discover the virus, but not its origins. At first, they try to cure it, but once the actual invasion begins, they release the version that several governments had been experimenting with. The modified version affects a much wider population, and seems to remove the degenerative mental aspects. Human governments start by infecting volunteer soldiers, then when things look grim, all their soldiers. When the tide of battle doesn't appear to be turning, they release the virus across the planet, infecting every human through high atmospheric distribution.
Now the last chance to save humanity are normal people with their normal problems, who just happen to have been infected and changed by an alien virus that has been modified by their leaders without a clear understanding of what they've done.
Or the group could be a group of randomly selected humans (the crew of a cruise ship, the passengers and crew of an airliner, a group of people on a weekend camping trip, anyting that could give us a wide slice of life), brought aboard an alien ship, modified to survive the rigors of an alien environment, tested to see if the lifeforms that had been seeded across the galaxy bred competent, adaptable warriors. They find themselves with superhuman abilities, pitted against alien combatants, and through sheer human adaptability and ingenuity, survive to prove humans are the greatest warriors the alien program bred.
From there they could be returned to Earth, or left in an armpit sector of galactic society to await their fate, while the aliens make plans to harvest all remaining humans from Earth. You could have space adventures or Earthbound adventures, characters from a wide variety of backgrounds with a wide variety of personality types, yet an event and future threat that keeps them bonded together despite their differences.
That last one could be your superhero AND sci-fi all in one.