The first thing that came to mind for me (other than a CNC router) is a simple jig. Use a suction cup meant for the glass/glazing industry, with a pivoting beam attached to a good router with a 2-flute carbide 1/4" bit. Suction the jig to the face of the plywood, turn the router on and rotate the beam-mounted router around the center until you get a circle. No center hole, clean cut, and you can fix the beam to any length you want to vary the diameter of the circle. A good bit should be able to cut through 1/2" plywood in one pass, or just adjust once and make a second pass.