We present a geometric framework in which spacetime emerges from correlated complex phase fields rather than being prescribed as a background structure. An induced metric arises naturally from phase gradients and generically undergoes degeneracy when phase correlations develop. We prove that metric degeneracy necessarily generates kernel directions supporting finite coordinate displacement with vanishing induced length. By introducing a normalized degeneracy proxy and a minimax bottleneck formulation, we demonstrate that near-degenerate regions form connected geometric channels linking distant points through uniformly suppressed metric determinants. Extensive numerical simulations confirm the spontaneous formation of such channels and their strong connectivity properties. To assess geometric regularity, we compute curvature diagnostics along bottleneck-optimal paths. In two dimensions, the Kretschmann scalar reduces exactly to the square of the Ricci scalar, enabling a direct invariant test of singular behavior. Across wide parameter ranges, curvature invariants remain finite and well-controlled despite strong metric collapse, indicating that degeneracy-induced adjacency does not rely on geometric singularities or exotic energy concentrations. The results establish a minimal closed mechanism linking emergent geometry, metric degeneracy, kernel-mode transport, and physically admissible nonlocal geometric adjacency within a unified phase-field framework.\vspace{0.5em} \noindent\textbf{Keywords:} emergent spacetime, metric degeneracy, phase fields, geometric adjacency, curvature regularity