I thought I responded to this earlier, but it looks like I didn't, sorry! In short, it's solvable in theory. The game as it's currently played has a finite game

I thought I responded to this earlier, but it looks like I didn't, sorry! In short, it's solvable in theory. The game as it's currently played has a finite game tree (thanks in part to the 50-move rule) and that finite game tree can in theory be brute-forced. In practice, I think it's one of those problems that's so large we can't possibly solve it. For an idea of the scale of a complete solution, solutions for all positions with 2 kings and 4 other pieces occupy ~100GB and solutions for positions with 2 kings and 5 other pieces are ~10 TB and it's believed that 2 kings + 6 will be in petabyte scale.