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The standard ΛCDM model is increasingly challenged by profound observational anomalies, most notably the Hubble tension and the unexpected discovery of mature, massive galaxies in the early Universe by the JWST. In this paper, we present the Topological Unfolding Cosmology (TUC), replacing the phenomenological ”dark sector” with purely geometric and thermodynamic dynamics. By modeling the Universe as a macroscopic Ginzburg-Landau vacuum undergoing a deterministic k = 2 → 3 topological phase transition, we seamlessly resolve the Hubble tension via the dynamic contraction of the sound horizon. Furthermore, we identify Dark Energy as the macroscopic topological latent heat of this transition, and replace Dark Matter with macroscopic topological tension originating from Kerr singularities. Crucially, this framework naturally predicts the exact statistical distribution of cosmic voids and the alignment of the earliest massive galaxies along primordial tension lines, offering a highly falsifiable, comprehensive paradigm shift in modern cosmology.