Your right, on the technical level. Europe with its never ending wars (only be intermitted by short truces) was well ahead of the U.S. in that regard. But on the tactical level Prussia, until it started its war series, wasn't known for ability to put up a fight (Yes, Frederic the so called Great, but during the Napoleonic wars its performance was rather lackluster).

So the German High Command had its time to learn how to mobilize, equip, march, motivate, supply and prepare an army for battle. And they had an established High Command. And they had an established military culture. The U.S. didn't have a large scale war in its history until then and I don't count the Mexican - American war large scale war.