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I feel like you could do this with some kind of stereolithography process like in semiconductor processing... You could very easily create the green, hole, and putter at astronomically tiny scales as microscopic thin slabs of silicon, but the roundness of the ball, I don't know enough about the specific processes to know how you might go about that. I'm sure it'd be possible with enough smart people thinking about it, though.
Actually interacting with this game, though? Are you imagining like Atomic force microscopy, a tiny tiny little putter attached to a much larger macroscopic assembly able to be manually manipulated?
Yeah, I mean I wanna putt somehow in someway, it is minigolf after all.
Perhaps a single molecule of buckminsterfullerene would work?
https://www.sigmaaldrich.com/US/en/product/aldrich/483036
~$200 for 8.3e20 tiny golf balls? Pretty good deal if you ask me.