We present a self-consistent cyclic cosmological framework that resolves the origin, nature, and observed abundance (∼ 85%) of dark matter without introducing hypothetical elementary particles. We propose that dark matter consists oftopologically neutral solitonic states (ΦDM) produced exclusively within black holecores from preceding cosmic cycles, where unphysical singularities are replaced bya finite Planck-density threshold (ρPlanck). Protected by a conserved topologicalwinding number W ∈ Z, these states are immune to perturbative decay. We introduce the Cyclic Distillation mechanism, showing how stochastic fluctuations within black holes break matter-antimatter symmetry across cycles, exhausting antimatter while leaving a residual baryonic fraction (∼ 15%) and an accumulating dark matterbackground. Under Loop Quantum Cosmology (LQC), the bounce density remains strictly lower than the black hole internal core density (ρbounce < ρPlanck). This Differential Stability Threshold ensures the dissolution of geometric event horizons and the liberation of ΦDM without disrupting its topological structure. The quantum gravitational wave energy released during horizon dissolution drives cosmic expansion and naturally reheats the universe without an inflaton field. Finally, we model intra-cycle accretion, demonstrating how progressive mass-spectrum shifts culminatein an eternal, entropy-resolving final collapse.