Super glue the button onto the recessed part of the top piece.

The project file has all the settings that met my needs. It has a few modifiers that clean up my mistakes as a designer and make specific parts different colors.

The pictures have fuzzy skin and random seam position for a more deliberate look.

I use Burger Tokens 22S Perfect Fit boxes: https://burgertokens.com/products/perfect-fit-deckboxes?variant=31359439274073
The design was created with these in mind.

You could also get away with these: https://makerworld.com/en/models/763762-mtg-cube-locking-reusable-pack?from=search#profileId-914402
BUT you'd have to shrink them by 1%. They "fit" if you push hard enough, but you might not get it out!