Thermodynamic and kinetic analyses based on our first-principles density functional theory calculations are used to interpret the experimentally observed formation of Cu carpets intercalated under the top layer of a 2H-MoS2 substrate. Spontaneous Cu transport from Cu pyramids on top of the MoS2 substrate through surface point defects to the growing Cu carpet is shown to be driven by a slightly lower chemical potential for the Cu carpet. We demonstrate that the competition between a preference for a thicker Cu carpet and the cost of elastic stretching of the top MoS2 layer results in a selected Cu carpet thickness. We also propose that Cu transport occurs primarily via vacancy-mediated diffusion through constricting point defect portals.