A belly door that opens at slow speeds and leads to a narrowing cavity—inverted diffuser.
In essence, the same as the F1 image above, but enclosed since there's no ground. And inverted since we need lift, not downforce. An F1 car's ground effect is the opposite of a plane's ground effect. The door is to stop its operation at high speed.
Theory of operation
The narrowing cavity will speed up the air, the air in the cavity thus will lose pressure (potential energy tuned into kinetic), the air outside the plane and underneath the cavity will be higher pressure, forcing the plane up.
There's no mission, just an experimental racing Howard Hughes kind of thing.
The engineering why is higher top speed, and low angle of attack slow flight.
The way I see it at slow speed the center of lift will shift aft, thus lowering the required angle of attack, I'm not sure about the longitudinal control authority and stability though.
Also, there'll be no need for high-lift devices and their associated systems, and possibly shorter wings, thus shedding weight and increasing top speed.
Can it fly? Are the assumptions above correct?
Engine location, nose gear location, etc., are not part of the question, just a pure aerodynamics question if we can make a cavity produce lift.