There must be hundreds of things that are the most quintessentially American thing while also being popular in the rest of the world.

The only thing I can come up with about which you could credibly say that "there is perhaps nothing more quintessentially American", is American Football. Literally the entire rest of the world plays regular football instead. There are American Football leagues outside the US (or there is at least one), but my impression is that they rely very strongly on American athletes who couldn't quite make the NFL.

Everything else that feels quintessentially American (apple pie, fast food, ketchup, fish sticks) is less quintessentially American than that.