If it's military might, that may be surprisingly irrelevant as the next century unfolds.
This. US and USSR were considered, rightfully, the superpowers during the cold war. "Sole superpower" simply means one has fallen, so the balance has tilt in favor of the US.
It wasn't "self proclaimed". It was globally accepted. It plays into American's patriotism but also flames anti-American in a lot of places. If you think it's just American manufactured claim you're mistaken.
In the same vein, China is considered "new superpower", also rightfully, considering how they have aggressively expanded their influence around the world.
The typical justification is that the US is the only nation that unilaterally harasses nations on the other side of the world. When the Russians and Chinese harass other nations those nations are in the same region. When the British feel like making an example of out a country in "our" hemisphere they get permission first.