Keep in mind the late 19th and early 20th Centuries were still the era of limited war based in large part on the model of the wars of German Unification. German plans to invade the Eastern US were not geared toward conquering the United States. They were limited operations designed to get a German lodgment somewhere on the east coast of the US, probably on Long Island, digging in, and generally being hard to expel without considerable and costly effort. From their the US was supposed to choose the negotiate with the Germans and in exchange for the Germans packing up and leaving the US would hand over some of its recently won gains from the Spanish-American War.
Yes, still a pretty nutty idea but not given the strategic thinking of the time (remember these were some of the same brains who thought WWI would last six months tops) it's not hard to see where somebody could think up something like this.
Another thing to consider is that the Germans can't even maintain naval superiority in terms of numbers - For ships commssioned by (the start of) 1900, you had 4 US predreads vs 5 German predreads. For ships commissioned by 1901, you had 7 US predreadnoughts vs the 6 German ones. For ships commissioned by 1902, you had 9 US predreads vs 9 German predreads. For ships commissioned by 1903, you had 10 US predreads and 13 German predreads. That covers the immediate scope of the timeline, so both sides are neck and neck in respect to absolute numbers of capital ships (The US had 2 additional ships under construction in the scope of the timeline - the Germans had 2 additional ones as well - later classes were laid down towards the end of our period and would be affected by war).
The US also has the advantage of fortified gun batteries on land and the possession of a variety of monitors as well. 6 monitors are in commission, of which 2 (one of which,
Monterey, is the newest) are assigned to the Philippines
. These vessels are older, but their munitions are fairly modern. Additionally, 4 more monitors are under construction (one on the Pacific coast), of which carry the most capable naval guns in the US armament. These would be ready by 1903, roughly, depending on if the war accelerates some under construction.
If we look further down at protected cruisers, the US maintains 13 protected cruisers, plus the 3 ABC cruisers and 2 bought from the British in 1899, for 18 total. 5 of those are unprotected cruisers / merchant vessel hunters. I'm also excluding
Vesuvius as she is a... unique vessel. The Germans maintained 8 protected and 9 unprotected cruisers, for 19 total. There Germans also had 7 light cruisers that would be completed by 1902 (mentioned as none additional were completed by 1903 - so an advantage there. This excludes armed merchant vessels.
For armored cruisers, the US depended on two old armored cruisers, while the Germans would have 2 new ones complete by 1903. But, depending on time of completion, they might not be available.
Not to go any further down into smaller vessels (which the US would have more of available due to that simple range factor - even the larger predreads will, at best, struggle to make the 3,742 miles as the crow flies from Wilhelmshaven to New York), but just making the point - you had a peer opponent in the US. The best thing for the Germans would be to try and press against the edges of the new American colonial possessions in the Philippines and etc. To land in the US means to defeat a peer opponent at the end of your logistical train and at his front door, and to do it in such a fashion that they have no ability to strike back. And to do that, you have to render the US's navy completely ineffective and to eliminate the entirety of their naval production, which is spread along a coast hundreds of miles long on the East Coast, not to mention facilities on the West coast. That requires not one lodgement, but multiple lodgements in the same locations that the US has been most pointedly preparing for invasion for decades (New York, Hampton Roads, etc).
And let's not even get into the fleets being less effective at a longer range, or a complete dedication of the German fleet meaning that they would have to denude Germany or the colonies of vessels - or how the coastal defenses (both static and mobile, in terms of monitors/coastal battleships) will not be travelling far from US waters, meaning the force multipliers stack
It's why this argument turns very quickly into a joint Anglo-German invasion, as there is no practical way for the Germans to enact such an invasion except to hope for the US fleet to sink itself.