One distinctive feature of the disordered systems is the breadth of their dynamics. It includes picosecond vibrations up to processes, involving the rearrangement of the nanostructure or the diffusive transport, which become observable only over extremely long times, i.e. even weeks or years. Numerical simulations and experiments evidence unexpected strong correlations between the picosecond and the ultra-slow dynamics for a wide class of disordered systems. Here we show that the fast wiggling of the atomic or molecular constituents provides a predictive tool of creeping phenomena. The fast predictability of the sluggish dynamics suggests novel routes to tackle complex cutting-edge applicative problems, like the longevity of the data stored in optical media and the long-term stability of biomaterials like food, drugs and vaccines.