This is easily done, Peter. It will be a tad expensive but the total cost depends on the size of box.
There are 2 kinds of expoxy. The kind like Bondo, which comes in a liquid form and a filled form as well as a gel form is relatively inexpensive but does have a strong odor until it has cured. The other kind is a true epoxy and it usually comes as a liquid. Industrial supply houses stock this kind, as do boat stores. The industrial places also stock fillers for if you want to thicken it or make it more sandable. You could also apply a layer of fiberglass to your project if you wished. This kind has a very low odor and twice the strength of the other kind. It is also twice or more as expensive.
Fastening your box together can be easy or very difficult. Since any water seepage into the plywood later will cause problems, glue the plywood together with the epoxy. It can be bought with various working times and your mix ratios can be changed a little to change the setting time but not as much as the other kind of epoxy. Talk to a good industrial supply house if you can. You can also make a closed box with one side openable, if you choose. Oil, grease and Saran wrap don't stick to it. Don't use wax paper because the wax will also melt into the epoxy and weaken it.