We present a transferable graph neural network (GNN) surrogate framework for molecular dynamics (MD) that directly predicts atomic displacements and propagates atomistic configurations without explicit force evaluation or numerical time integration. The central objective of this work is to establish whether a common GNN formulation can represent atomic dynamics across materials with fundamentally different crystal symmetries and coordination environments. The same network architecture, feature representation, graph construction, and training protocol are applied without symmetry-specific modification to face-centered cubic (FCC) aluminum, body-centered cubic (BCC) iron, and hexagonal close-packed (HCP) magnesium. Across these distinct elemental and crystallographic systems, the framework achieves position-prediction errors on the order of 10^-4 Angstrom^2 and supports stable autoregressive propagation to nanosecond time scales. The predicted trajectories preserve thermodynamic stability, characteristic coordination-shell structure in the radial distribution functions, and temperature-dependent mean-squared-displacement behavior. In particular, the framework captures the closely spaced coordination shells of BCC iron and the anisotropic coordination environment of HCP magnesium without introducing lattice-specific representations. These results demonstrate that direct GNN-based atomic propagation can be formulated as a transferable framework across different elements, lattice symmetries, and coordination geometries, providing a pathway toward generalizable surrogate models for accelerated molecular dynamics.