My daughter uses storage containers for her two rescue cats (they are both adults) and use the same litter box.

She cuts a hole in the TOP of the container lid.

We all know how cats love to climb so it is no problem with them figuring out the opening leads to the litter box. When they're getting out, any litter stuck in between their toes usually winds up on the "lid" of the container, resulting in very little litter on the floor.