We were projecting power WAY before the Spanish American War. The Monroe Doctrine was all about power projection. We send gunships into Japanese harbors to force them to open ports to western trade. That was power projection. We had spheres of influence in China. We invaded Mexico multiple times. Manifest Destiny was a century-long policy of power projection across a continent. Hell, the first war we got into after independence was power projection in North Africa, a decade before the War of 1812.

The US has ALWAYS projected force outwards towards other nations. We notably avoided direct conflict with European nations when they were militarily, economically, and geopolitically more influential than us, but there's a hell of a lot of world that isn't Europe.