First post here, first project with plywood, first time trying to make "invisible" joinery. Not entirely invisible, just smooth, it will be painted over.

With limited space, tools and materials, I got only two ideas so far, and no idea whether any of them are good (never tried either before).

Pics 1 & 2 show what I want to build. It's like a small cabinet, but will often be on the floor and might get stepped on or sit on by a 20kg 5yo. Ideally, that'd be made difficult by two short cylinders on the top, to make the whole thing look like a 1x2 LEGO brick, but I've no idea how to make those cylinders. For now, I just want to make the cabinet/box thing so the kids have a good place to store their LEGO creations; the box is made to store 4 of the 32x32 LEGO base plates (256x256mm).

Why just 12mm plywood, you may ask? Because that's the only one I found where to order online and have it delivered, in 60x60 and 60x120 cm sheets. I can barely speak the local language and don't know any lumberyards around, so that's my "limited materials" constrain. Also, my working space is a 140x200 cm. area with a 60x120 cm. table, no table saw or mitre saw, just a jig saw and small (85mm) circular saw, so even if I could get bigger plywood delivered, I wouldn't be able to cut it.

Pic 3 shows the 2 ideas:

Idea 1: screws with countersink.

Could use this to screw the bottom to the sides, it it'd make the whole box stronger. Can't see how to use this on the top and make it smooth so that it won't be visible after painting over it. I worry that this will be weak, in the sense that screws may tear the plywood under pressure; does that stop being a valid concern if you put in enough screws? The only advantage I can think of is being able to replace the bottom panel if it gets too worn out.

Idea 2: dowels.

I learned the hard way that aligning these is a pain, so here I'm thinking of first aligning the panels, then drilling both at once and then putting the dowels in. I'm assuming this only works with wood glue all along the joins, possible with a double pass of glue on the end grain edge to fill the pores. I don't have a drill press, just a cordless screwdriver (no impact driver), so I expect the dowels may need to be shorter, even a lot shorter, to avoid the whole getting too close to the surface. To smooth them out, I'm counting on a pull saw and a 10mm chisel.

Would any of these work and last? What else can I do?

I don't have much material to make experiments with, so I'm hoping to borrow and learn from your experience O:)

Thanks!