Sand the surface of the plywood with 80-grit sandpaper.
Combine wood filler with some of the sawdust in a small container. This ensures the color of the filler matches the plywood.
Fill a syringe with the wood filler. You can find syringes at woodworking shops or home improvement stores.
Lift the edge of the one sheet of plywood until you can insert the syringe over the void. Inject the filler into the gap and fill the void until the filler is flush with the surface of the wood.
Apply a layer of adhesive on the surface of the bottom piece of plywood. Clamp the sheets together overnight while the adhesive dries.
Fill voids on the outside layer of plywood by inserting enough putty to cover the void. Use a putty scraper to smooth the putty flush over the hole and wipe away any excess.
Rub the outer surface with the sandpaper to blend the filled hole to make a smooth surface. Sand the edges for a smooth finish. Wipe away sawdust with a tack cloth.