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Geometric deep learning has advanced computational materials science, yet most existing approaches remain constrained by the periodicity assumption inherent to crystalline systems. While crystal-based graph neural networks exploit translational symmetry and periodic boundary conditions, amorphous materials—such as glasses, liquids, polymers, and disordered alloys—lack long-range order, exhibit non-repetitive atomic arrangements, and span widely varying system sizes. This mismatch renders periodicity-dependent methods both theoretically inadequate and practically unreliable for disordered structures. This work identifies three key distinctions—non-periodic graph construction, symmetry limited to E(3) equivariance, and non-physical boundary conditions—which collectively give rise to fundamental challenges, including scaling limitations, loss of transferability, and structural representation imbalances. Through theoretical analysis, the limitations of crystal-oriented graph neural networks in amorphous settings are clarified. To address these issues, a new framework is proposed based on size-extensive, E(3)-equivariant architectures that eliminate periodic assumptions and integrate multi-scale encoding of local, intermediate, and global structure with size-normalized aggregation. This formulation provides a principled foundation for geometric deep learning models tailored to amorphous materials and their applications in energy, optics, and structural systems.