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You'd have to boil the concept of minigolf down to the barest aspects and ask yourself how much each can change while still qualifying as minigolf. Can the "ball" be an electron? Can the "putter" and "hole" be electromagnetic fields?
Not OP, but I'd be more interested in making a tiny ball round enough to roll across a surface and fall into a hole (not the "absence of an electron" meaning of that word). And I'd want it achieved through gravitational forces rather than electromagnetic. I feel like that makes the problem harder and largely makes it a materials science question. Someone in MEMS research probably has a good idea of how to approach this.
With those parameters, the system would probably need to operate in a high vacuum with as little interaction from electromagnetic forces as possible. All materials used should probably have a low permittivity to reduce the amount of static charge buildup from friction. Intuitively, I feel like it makes sense to use the same material for everything. But it might not be that simple. Maybe the material used to make the smallest round ball isn't well suited to making the smoothest surface for a short putting green?
I dunno, I'm just a guy who took a few classes on semiconductor design in undergrad spit balling.
Ok I am am sort of big picture more interested in what philosophically is the miniest minigolf you can make with it still being golf with a "ball", a "club" and some minimal course that must be navigated to a "hole".
I am fascinated by your question as well though. I would imagine it might come down to manufacturing a ball from a non-crystal lattice like glass to get it as small as possible while still being a ball?
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?
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.
Yeah, I mean I wanna putt somehow in someway, it is minigolf after all.