Big plot issue: figuring whether and what. They can have you try to pick up something to see if you are strong; run, if you are fast; go into the dark to see if you have nightvision. But some are more complex. You discover you can talk to wombats if you go to the zoo, perhaps -- or a kind of Australian ant if you go to Australia. Invulnerability? That one's tricky.
Some people theorize that they all get powers, it's just that some never hit the right circumstances.
Also, there is a superhero in this story that can detect people with powers. So, all right, the power is latent until it first gets used. . . .
Hmmmm. . .
Some people are going to say that the power is triggered by the circumstance, and if you had met a koala first, you would be yammering to koalas instead of wombats.
And everyone who's ever been supersick might manifest a power someday which makes life tricky. Though I could lay down a rule where major powers come early and after a month or two, you start to get people who only realize they can always tell where north is, or don't get sunburned, or poison mosquitoes that bite them.
On the bright side, it does give governments another good motive to keep people from being exposed. Besides the dislike of destabilizing superpowers. They already had one: at least three times, people have turned into enormous natural disasters. Now, they also have to worry about idiots who kill themselves by jumping into a fire to trigger fire immunity -- and don't get it. (And some of those insist that the testing is carefully calibrated to avoid getting powers too wonderful.)
And while we're at it, this has gone on only twelve or so years. How long did it take them to realize that the sickness makes you immune? Or that the big powers come quickly? Hmmm. . . . .
On the bright side, if you've been sick, and don't get powers, you do have one. You can offer to work for superheroes as a specially immune person, because the circumstances revolve about them.