Re: ROTFL I mean SRVL
"Easy. Just make the wings a bit bigger. "
A quick play around with an online lift force calculator suggests that, at typical sea level air densities and assuming a lift coefficient from a fully flapped and slatted wing of 3.3 (taken from the most optimistic looking plot of lift vs angle of attack I could find without spending much time on it), a 20 tonne aircraft travelling at 35 knots would need a wing surface area of around 300m^2 to maintain level flight.
Wiki suggests the F35A has a wing area of 42.7m^2, and I don't think there's much difference between the A and B in this respect, so you're talking about making the wings a mere 6 times larger. Or, to put it another way, slightly bigger than the wings of a B767 airliner.
So yes, theoretically speaking, it seems like it would be possible for a 20 tonne aircraft to fly at 35 knots just on wing-generated lift. Practically speaking OTOH...