ML/NJ
If a 2.2 kg cube stands on a scale, it imparts about a pound of force due to the acceleration of gravity on the mass. If another 2.2kg block sits on top of the first the combined force is 2 lbs. As more and more blocks with the same mass are stacked the force increases. When the stack gets up to several dozen miles each additional block adds less than 1 lbs force because its distance from the center of mass causes its acceleration to decrease. But the weight on the scale is the sum of all the individual forces.
Now start at the top of the crust. A 2.2 kg mass of dirt exerts about a pound of force on the column of earth beneath it. Move in. A 2.2 kg mass of dirt underneath the first exerts about a lb of force on the column of earth beneath it. The two combined exert about 2 lbs of force. Repeat this exercise all the way to the center of the earth’s mass. The force exerted by each mass will vary, near the center this force will approach zero, but the total force is the sum of each individual mass.
Repeat this in all directions and convert that force to pressure and that is the pressure at the center of mass. Certainly much more than zero.