Does a Go variant on an infinite board exist?
There are variants like 3 dimensional Go, which may be interesting to you.  However, from personal experience as well as seeing higher dans struggle, I'd guess humans are far worse at them than computers :)

I'm not aware of any kind of "infinite" Go that is even remotely playable. The basic problems are ladders, which need to end, and counting, which requires complete separation of space.

As far as I can tell, infinite Go could be achieved via a sequence of spaces that interact, either hierarchically or flat. You could define that a ladder may not leave its subspace etc. Play could either be simultaneous in all subspaces, or in only a selected (number of) subspace(s). While this seems borderline theoretical computing science, I believe it would provide a gameplay quite similar to the original, just with certain additions that make turns a lot more complex.