Their army was far better than the US Army, but the US Navy by 1900 was a solid match for the Imperial Navy. If we assume Britain is pissed enough at the US for whatever reason to stay neutral in the conflict, then Germany will do some serious damage before they bog down and are swarmed by the hastily reformed US Army. Their supply lines are mauled by the US Navy, which is laying down destroyers and light cruisers like nothing else. Give it 1-2 years, and Germany will sue for peace and lose its Pacific colonial empire to the US as a result of the end of the land operations (aimed at Virginia and New England) in utter defeat and probably a solid naval battle or two or three which sink some battleships in clear American victory.
If we assume a one-on-one fight, this isn't one Germany wants to fight. It could trigger a very bad scenario where toward the end (when they've sent a ton of men to POW camps and a ton of sailors and their warships to the bottom of the Atlantic), France declares war and the US completely backs them in this (perhaps for profit in the aftermath) and sends an expeditionary force of their now-experienced Army to Europe. Germany has minimal at best gains to make and utter disaster at worst to face here. It's one thing to intend to fight the US on the high seas and contest colonies and maybe shell some cities for reparations (like Italy came up with). It's another thing to try and mount an invasion of the US, a place where a hell of a lot of people have guns and which can hammer out more guns and arm/train/supply conscripts in a few months to simply overwhelm your beachhead in patriotic fervor, let alone what happens when the officers and higher ranks get a hold on things (like at the end of World War I) and the sheer US industrial capacity to supply this force when needed. And such a beachhead can't be supplied well, when the US already has a solid amount of battleships (too battleship heavy in some respects, granted) and the shipbuilding capacity to hammer out the rest of a navy, one which could match the Royal Navy, in a few years if needed (and matching the Imperial German Navy is far easier).