Americans are crossing the borders by car every day,
Heck, I live here and I don't know of any Americans crossing the border - much less every day! The bottom-line is - CURRENTLY - in The Netherlands, Americans are not allowed to enter the country unless you are performing an essential function, have a dual passport, or a long-term resident visa. (and those are just a few of the "exceptions" but the others are fairly impossible for most Americans).
If you meet the VERY LIMITED restrictions currently in place, you still need a negative COVID test to enter the country. Thalys and other "pass-through" transportation options are required to check before travelers board and exit is restricted inside the NL. The same goes for Schiphol where documentation is required.
Now, are they checking those docs as they should? Probably not so much... but if they do, that's a bad day for you. We've lived through 15 months of restrictions and in the last 6-7 months, they got tighter and tighter until it became impossible for us to travel. (Getting back in the country was quite challenging due to the testing requirements - which was the goal of the Dutch government to restrict travel, to reduce the soaring COVID numbers). Surprisingly, one of the easiest countries for us to travel to during this period - for us - has been the USA! But we also have US Passports and long-term residence Dutch visas.
If you are caught here, there is a fine. (It starts at 330€ per person, per violation). I suppose that, if they took this as a Schengen violation, then you could also face another fine, deportation, and a ban for re-entry to the Schengen zone for XX years. It's not been done yet (to my knowledge), but the locals are very frustrated by the last 15 months and won't have much sympathy for someone who intends to violate the rules they have been forced to follow.
But wait it out --- this will probably all change by July. And this will be moot!