Well for a minimum, we need the maximum exerted force on a single point on the Earth (Say a really big mountain, I don't know if everest is the heaviest feature, but for this let's assume it is) once the weight is measured we can work out the force downwards in Newtons, all we do then is work out at what depth the pressure becomes identical with the upthrust from the material below it, if the material remains consistant (or thereabouts) then twice the depth to get to this level point from sea level is the minimum thickness of the Earth...
shame I have no idea how this could be tested practically :S...