We demonstrate that quantizing Einstein's equation by promoting the cosmological constant to a quantum operator leads to a suppression of its effective value, providing a potential resolution of the cosmological constant problem. Considering an inter-universal interface that separates causally disconnected universes in the gravitational path integral implies a loss of classicality and uniqueness of gravity in the vicinity of such an interface. Stationary-phase arguments then show that the phase contribution from a family of small positive values of the cosmological constant dominates the path integral. This results in a quantum-dynamical selection of the cosmological constant, yielding a non-anthropic suppression mechanism within four-dimensional gravity.