  Glasses are out-of-equilibrium systems aging under the crystallization
threat. During ordinary glass formation, the atomic diffusion slows down
rendering its experimental investigation impractically long, to the extent that
a timescale divergence is taken for granted by many. We circumvent here these
limitations, taking advantage of a wide family of glasses rapidly obtained by
physical vapor deposition directly into the solid state, endowed with different
"ages" rivaling those reached by standard cooling and waiting for millennia.
Isothermally probing the mechanical response of each of these glasses, we infer
a correspondence with viscosity along the equilibrium line, up to exapoise
values. We find a dependence of the elastic modulus on the glass age, which,
traced back to temperature steepness index of the viscosity, tears down one of
the cornerstones of several glass transition theories: the dynamical
divergence. Critically, our results suggest that the conventional wisdom
picture of a glass ceasing to flow at finite temperature could be wrong.
