I'm not sure how to address that within the scope of an HN comment (and I don't think I have the time). To start with the problem is severely underspecified.

What do you mean by "infinity" exactly? 2^64? 2^128? Any arbitrary bigint? Periodic boundary condition?

Why perfect mazes - does that really matter? Are these supposed to be human solvable or is this some sort of abstract art? Anything human solvable requires at least one path of (very) finite length from start to finish.

Overlapping tiles and doing nothing else produces multiple paths. It's the quick and easy solution if the goal is practicality of implementation and human oriented puzzles.

If you insist on a perfect maze an obvious solution is 2^64, a periodic boundary condition, and a space partitioning tree with many children per node (ie n >>> 2). Connectivity is determined at each level. Long uniform walls can be reduced or even eliminated by warping block boundaries in various ways; among other things, you could potentially use the maze solution at each level to assign node membership for the next level.