Maybe leave on the porch light and open the door with the screen in place. He's gotta get hungry some time! That's where I often see tree frogs here, except they are on the other side of the screen.
Tree frogs are loud and nocturnal. Check your drains, showers, house plants. At least that's where I have found them after a few weird nights. If you have cats, pay attention to where cat is staring.