Cut the Plywood
Before cutting the plywood, make sure you keep in mind the outside dimensions of your box. It's important. For instance, the depth of the wall cavity into which the niche box is to be placed is the width of a typical stud or 3-1/2 inches. That means that the outside depth of your box can be no more than 3-1/2 inches, which also means the inside depth of your box will be that dimension less the thickness of the back panel (3/4") or 2-3/4".
For the top and bottom panels of the niche, cut two pieces of 3/4" birch plywood to 26-1/2" (or your desired measurements) and 3-1/2" wide. For the sides of the box, cut two more pieces to 18" x 3-1/2".
Now measure and cut the back panel out of 3/4" plywood.