in a situation where said government isn't depicted as fighting evil aliens/terrorists/what not (so that despite being a superpower, it still can see itself as the underdog)

This made me think back to Independence Day in which not only are humans the underdog by default, but iirc, the destruction of most major cities early on means that “the American Government” basically consists of the President, a handful of advisors, and a small airforce that’s about 50% civilian or retired pilots who’ve volunteered.