The discrepancy between early-universe (H0 ≈67.4 km/s/Mpc) and late-universe (H0 ≈ 73.0 km/s/Mpc) measurements of the Hubble constant implies a breakdown in the standard model. We propose that this tension arises from a geometric phase transition in the vacuum structure. We model the vacuum as a **Random Tensor Network** that relaxes into a Face-Centered Cubic (FCC) lattice. We provide a thermodynamic argument for this ground state, showing that the vacuum minimizes free energy by maximizing packing density (Kepler Limit) and isotropy (Oh symmetry), utilizing Cosmic Inflation as an annealing mechanism. We identify a topological transition driven by cosmic void formation, where the effective coordination number shifts from a shielded surface state (N = 12) to an exposed porous state (N = 13). This topological activation predicts an intrinsic expansion boost of 13/12 ≈8.3%. We validate the kinematic consistency of this geometry via a constructive simulation of 5,000 nodes which saturates at K = 12 without jamming.