It's a paradox: if the buoyancy--an upward force--results from the difference in water pressure on the bottom and top faces (the contribution from the side forces being horizontal), how can there still be buoyancy when there's apparently no water underneath the bottom face?
Consider what happens as the block approaches the bottom of the container: as the gap between the two shrinks, a slight excess in pressure develops under the block, forcing the water in the gap out the sides. This process continues until whatever high points that microscopically exist on the block and the container bottom begin to make contact with each other. As the contact force gradually increases, there is less and less weight left over to maintain the slight horizontal pressure gradient underneath the block, so the the rate at which water is squeezed out the gap decreases. The pressure under the block decreases, approaches that elsewhere on the bottom of the container, and when everything reaches equilibrium the pressure underneath the block, pushing it up, is the same as it would be if the bottom of the container weren't there.
If you do something to relieve this pressure, you can indeed get rid of the buoyancy force. If, for example, after the block has settled into place, you cut a hole in the bottom of the container just inside the perimeter of the bottom of the block, the block will no longer experience a buoyancy force. Instead, the net force exerted on the block by the water is downward: it's the weight of the column of water above the block.