It's much better if it is screwed in than just sitting there. Mine kept trying to escape even with screws.
Two methods that might make this easy: If you have access from below it, you can replace the feet screws with longer ones that go through the floor of the cabinet and can be tightened from below. If the back of the cabinet is plywood, you can simply run two or three screws through the rear of the microwave, from inside with the door open, into the rear plywood wall. This is what I did after checking the construction of the microwave. The rear of the microwave was simply one thin layer of steel, with no wires or other components.
I only exaggerate enough to compensate for being taken with a grain of salt.