It seems like the problem is that each of the shadows is individually powerful, and we have no way to track them all down, and also there are thousands of them, and also even if we somehow killed them all we'd just be hit by a different wave from a different outbreak.
I see three possibilities here:
1) There isn't a solution and the Gamemaster wants us to realize that, and then we'll do small excursions in a doomed world.
2) There's a particular solution that the Gamemaster has in mind, but they want to see if we can come up with it, and also impress the difficulty of the problem so that we're suitably impressed by their plan.
3) The Gamemaster doesn't already have a plan for the shadows but wants to give us the chance to find one if there is one, just in case.
My money's on number 1; we're only level 3 right now and it'd be a weird campaign if high level wizards fixed the inciting incident without us playing any major role.