A key bottleneck in solid mechanics is to bridge the many decades in time-scale between computed atomistic elasticity and experimental mechanical testing in real materials. Atomistic simulations as in all molecular dynamics (MD) computational protocols suffer from limitations due to the time-step used in discretizing the equations of motion for the atoms in the material, which is of the order of femto-seconds, thus resulting in astronomically large deformation frequencies probed by MD (in excess of Tera Hertz), whereas the available experimental data are in the sub-Mega Hertz region, hence many orders of magnitude lower in deformation frequency/rate. We show that, by exploiting the mathematical description of non-affine atomic-scale displacements under deformation, the intrinsic limitation to atomistic MD computational protocols can be avoided, which opens up the way for the atomistic computational description of mechanical response at experimentally accessible frequencies. We use polymethyl methacrylate (PMMA), a polymer glass, as the model real-life material for both experiments and atomistic computations. We employ a time-dependent memory kernel within the framework of the atomistic Generalized Langevin Equation in non-affine lattice dynamics (NALD), which provides the complex modulus and thereby enables the evaluation of the shear and Young’s moduli as functions of both deformation frequency and temperature across an unprecedentedly wide range of time-scales. Overall, NALD allows us to bridge the time-scale gap between MD simulations, ultrasounds, Brillouin scattering, ballistic testing, and standard mechanical testing of real soft materials, and provides a theoretical description of the mechanics of polymers over nearly 20 orders of magnitude in deformation frequency.