when it comes to exterior projects, especially ones that use plywood,
I suggest a person look at "how to build a boat transom" or - "how to build boat seats".
these two items live outside in a pretty demanding environment.
I used to use a good grade B/C exterior grade pine plywood and sealed with a deep penetrating mix of a few items listed below.
with the advent of so much new junk plywood from other countries now, I am afraid to use it for myself, much less recommend it to someone else without knowing exactly how and where it was made. even the so called "marine plywood" is under attack with counterfeit products that will fall apart when wet.
(of course, the "go to" would be MDO exterior sign grade plywood).
anyway, you can mix up this concoction and test it on some scrap plywood and see how you like it. (this is just the waterproofing sealer - not the final finish).
and to add more confusion: there are literally hundreds of wood deck sealers on the market today. each saying they are better than all the rest. (so who knows).
what gets me is people pay thousands of dollars for a new wood deck, then waterproof it and seal it and stain it . . . . but, what about the bottom of the boards ??
and after thoroughly sealing the plywood and flooding the edges, let dry/cure for a day or two. (3 or 4 is better). then force a quality exterior "paintable" caulk into the edges with your finger - let that cure according to the instructions on the product you use.
then - prime and paint like any exterior project.
looking forward to seeing your project .