The sky at MeV energies is currently poorly explored. Here we present an innovative mission concept and we outline the scientific motivation for combining a coded mask and a Compton telescope. The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO) is a novel concept for a next-generation telescope covering hard X-ray and soft gamma-ray energies. The potential and importance of this approach that will bridge the observational gap in the MeV energy range are presented. With the unprecedented angular resolution of the coded mask telescope combined with the sensitive Compton telescope, a mission such as GECCO will finally disentangle the discrete sources from the truly diffuse emission, unveiling the origin of the gamma-ray Galactic center excess and the Fermi Bubbles, and uncovering properties of lowenergy cosmic rays, and their propagation in the Galaxy. Individual Galactic and extragalactic sources will be detected, which will also allow studies of source populations. Nuclear and annihilation lines will be spatially and spectrally resolved from the continuum emission and from sources, addressing the role of low-energy cosmic rays in star formation and galaxy evolution, the origin of the 511 keV positron line, fundamental physics, and the chemical enrichment in the Galaxy. It will also detect explosive transient gamma-ray sources, which will enable identifying and studying the astrophysical objects that produce gravitational waves and neutrinos in a multi-messenger context. A GECCO mission will provide essential contributions to the areas "New Messengers and New Physics" and "Unveiling the Drivers of Galaxy Growth" emphasized in the Decadal Report on Astronomy and Astrophysics 2020.