how many of these boxes are you looking to build? What is the box size? cuting boards are HDPE Natural Plastic, which is realtively cheap depending on what thickness you buy. I think last time I bought it was about $70 for a 4x8 sheet that is 1/4" thick from piedmont plastics. That would be the best way to go. buying precut cutting boards is going to much more expensive.
In addition many plastic suppliers will precut the sheet into whatever size you want, (with cnc saws, only stright cuts) so if it is nothing more than a square box, you dont’ even need a cnc machine, you just need to weld to screw it together.
if you are looking at making a ton of them, you can get the same thing form china for about half the price.