A standard Cajon is not easily available in my locality. So I have started building my own, using plywood.
For the playing surface, the minimum thickness of plywood available is 4mm. Is it good sounding for the Cajon? Is there any alternative to plywood?
I certainly admire your resourcefulness and commend you on your willingness to attempt to build your own Cajon. I don't have the patience to attempt such a project myself.
You want the playing surface (known as the tapa) to be as thin as possible so that it will vibrate and resonate! A playing surface that is too thick will be less responsive and sound dull.
4mm is probably thicker than you want. You want as thin as possible. If the thinnest plywood available in your area is 4mm, then you will have to use that and it will work. But you won't get as much resonance as you would from a 2mm or 3mm piece.
If there is a hobby or model shop in your area you might find some thinner plywood there, or perhaps you could order a piece on-line and have it shipped. Plywood that thin is not always available at a building materials store because it is not something you would typically use in construction.
I recommend 4mm or 5mm for the back, and 9mm - 12mm for the top, bottom and sides.
One thing you need to be sure of is to use some wood glue to coat your screws and use some screws that are designed for wood and will grip tight. Also be sure to glue and screw the pieces together. A mitre joint or rabbit joint would be a good idea to join the pieces together. You will want to use a clamp to hold the pieces together while the glue dries.
If not properly glued and fastened together - when you start beating on it, the screws could vibrate and come loose from the vibration. I saw this happen on stage once with a musician who built his own cajon. It fell apart while he was playing it.
You don't actually want to glue the tapa (playing surface) but use really tight holding screws. Leaving the tapa unglued will allow it to vibrate a little more and allow you to open the box if you ever need to adjust the snare wire. Some folks even claim you can alter the sound by removing some of the screws or loosening a few.
There are many tutorials on line that will show you how other folks have built cajones. But they are not all good examples - so don't assume that any one particular method is best. Review many and perhaps you will get a consensus. If you watch the YouTube videos, pay attention to the comments. Some will have comments that indicate the video contains bad advice.
Good luck with your project!
I built a cajon prototype for which I tried 4mm tapa and it was too thick to resonate well. The switch to 3mm improved the sound quite a bit, though I'd probably prefer even thinner tapa.
If thin plywood is hard to get you could try using some other material for tapa, for example, a thin plastic sheet (I'd try 2mm polyethylene first, but that's not necessarily the right choice of the material).
I built a stomp box using cheap wall board, you know that stuff we all had on our basement walls in the 70s. It worked really good until it cracked from a year of being stomped on, but it is so cheap to buy I cut up a 4x8 sheet into several replacement covers,
The cheap rec-room paneling was made of luan mahogany, in tiny tiny layers! So, of course, it would do a really decent job on a Cajón. I wonder if an older vintage may be better wood than later years? But, if I had a piece of 70’s paneling, I would give it a shot. I might sand the “face” down to core wood and either paint it or put a solid wood veneer on top? One advantage of affixing the face with screws: it makes a decision easier, because you can make the faceplate with what you can find quickly, while scouting for better material. If I lived near a skateboard maker, I would ask if they could create a faceplate for me. Making skateboard decks uses the exact technology to make a great faceplate, just with a different wood, perhaps, and much thinner.
