We investigate the geometric origin of inertial mass within the Origin Geometry (OG) framework, in which spacetime is modeled as a discrete four-dimensional aperiodic lattice based on H₄ (600-cell) topology. Rather than treating mass as a fundamental particle attribute or a coupling parameter, we propose that inertial mass arises as a structural response of the lattice to metric deformation. By analyzing elastic eigenmodes and deformation spectra of discrete H₄ lattices, we show that excitations which necessarily distort four-dimensional volume experience large inertial resistance, while isometric and orientation-preserving motions remain energetically suppressed. Within the OG framework, mass is therefore identified as a measure of geometric stiffness associated with volumetric participation, independent of interaction dynamics or phenomenological inputs. The present work establishes a pre-dynamical definition of mass grounded purely in discrete geometry. It provides the conceptual foundation required for subsequent identification of heavy and light excitation regimes while remaining agnostic regarding particle composition, gauge structure, or cosmological interpretation.