Quantum Elastic Spacetime Theory (QuEST) introduces a first-principles framework for gravity by modeling spacetime as an elastic, quantum-deformable medium. Unlike classical approaches based on the metric tensor, QuEST employs a strain field σμν and a discrete configuration variable n(x) to describe both continuous and topological changes in spacetime. At high densities, matter injects energy into the spacetime fabric, inducing strain. When a critical saturation threshold is reached, the region undergoes a quantum rearrangement—removing singularities without invoking exotic matter or metric quantization. From its foundational Lagrangian, QuEST derives all key predictions without free parameters: gravitational wave echoes with delay τ∝M5/4τ∝M5/4 matching LIGO data to <1% error; a quantized black hole core with discrete modes contributing to entropy and echo radiation; a nonsingular cosmological bounce followed by slow-roll inflation; and scale-invariant primordial fluctuations from quantized strain, eliminating the need for an inflaton. The theory also offers a natural origin for dark energy via residual large-scale strain. All results follow from physically justified field dynamics using only fundamental constants. QuEST thus provides a unified, testable alternative to classical and loop-based quantum gravity approaches—recovering GR in the weak-strain limit, while resolving its singularities and predicting observable quantum gravitational signatures.