We present the Quantum-Elastic Geometry (QEG) theory, a unified framework wherein spacetime is modeled as a fundamental, physical substrate with quantum, elastic, and dissipative properties. The state of this medium is described by a single, symmetric rank-2 tensor field, $mathcal{G}_{muu}$, whose dynamics are governed by a generally covariant action. Known physical interactions are shown to emerge as distinct, irreducible deformation modes of this unified field: gravity, electromagnetism, and a new field --denominated "thermo-entropic field"-- that gives rise to irreversible thermodynamics.Furthermore, fundamental constants of nature are shown to be uniquely determined and interrelated by the substrate's properties. We derive the fundamental constants of nature through two distinct yet convergent approaches: (i) from the physical postulates of QEG, assuming the $mathcal{G}_{muu}$ tensor, its properties leading to dimensional collapse ($[M]equiv[L]equiv[T]$), and parsimonious physical principles (e.g., reciprocity, damped equipartition, self-consistency), we deduce specific functional forms for the constants; and (ii) independently, assuming only foundational geometric principles for the substrate (homogeneity, isotropy, covariance, Lorentz invariance) and imposing self-consistency -formalized via a minimal set of geometric normalization conditions consistent with the QEG framework-, we derive the substrate's emergent structure and properties, obtaining precisely the same functional forms for the constants. The outcome is a robust, convergent two-way deductive framework, in which fundamental constants are geometrically enforced, emerging as predictable consequences of a stable and symmetrically constrained geometry.Finally, we show how the theory predicts -among other results- a scale-dependent gravitational coupling derived from a geometric duality in self-energy, which offers a parameter-free resolution to key cosmological tensions, including the Hubble crisis.In summary, QEG provides a coherent and consistent origin for both fields and constants, unifying them as rigorously derived emergent properties of a single, dynamic spacetime substrate.