In a previous paper, we investigated the role of inherent structures in the vitrification process of glass-forming materials, showing that the dynamical transitions between inherent structures (states) can be well predicted by a first-order kinetic scheme based on infrequent-event theory at low temperatures. In this work, we utilize and extend that methodology in order to completely reconstruct the system dynamics in the form of the mean square atomic displacement as a function of time at finite temperatures on the basis of the succession of transitions in a network of states, the vibrational contribution being evaluated on the basis of short molecular dynamics runs artificially trapped within each one of the states. In order to do so, we provide the mathematical formulation for lifting the coarse-grained Poisson process model of transitions between states back to the atomistic level and thereby reproducing the full dynamics of the atomistic system within the Poisson approximation. Our result shows excellent agreement for temperatures around and below the glass transition temperature of our model Lennard-Jones two-component mixtures. Clearly, our approach is able to reproduce the full dynamics of the atomistic system at low temperatures, where the Poisson approximation is valid.