Standard modelling of the distribution of cosmic rays (CRs) throughout the Galaxy is based on a steady-state assumption, where the source spatial density is described using a smoothly varying function of position that does not evolve with time. While this is a convenient approximation, reality is otherwise where primary CRs are produced in and about highly localised regions, e.g., supernova remnants, which have a finite lifetime. With the latest version of the GALPROP code it is now possible to model the injection of CRs over a long time history from a distribution of discrete sources (in space and time) at high spatial resolution and calculate the associated non-thermal emissions from radio to high-energy gamma rays. This paper describes such modelling using time-dependent 3D CR source distributions and 3D models for the interstellar gas, radiation, and magnetic fields with the GALPROP code. The results presented in this paper have relevance for connecting data collected by GeV energy range instruments, such as the Fermi Large Area Telescope, with observations made at TeV energies by Cherenkov Telescopes, such as HESS, and the forthcoming CTA.