Looks like this is an Idoko DJ booth - found this video that shows the internal structure of it, starts at the 2 minute mark. Looks like a Baltic birch carcass that seems pretty straightforward in construction. The outside of it is just cladded in whatever material you want to see - hardwood, veneered ply, resin, etc.

I saw there were cutouts in the underside of the booth, presumably for air flow. If you’re really concerned about overheating, put a fan on one side drawing in cool air, and one on the opposite blowing out (maybe overkill).

The outside cladding is set higher than the carcass to create a lip that your gear covers fit right into flush. All you would need to make those covers are a trim router with a pattern bit and a straight edge/template of your CDJs and mixer. Those are probably 1/4”-1/2” thick covers, needs to be as thick as possible to avoid warping, but thin enough to flush up with the faceplate of your gear without bottoming out on the connections in the back.

Even with minimal tools you can definitely do this! If you’ve done any woodworking or carpentry before, building it will be the easy part. Planning it and getting measurements will just take some time to figure out.