Context. The High Energy Stereoscopic System, the Major Atmospheric Gamma-ray Imaging Cherenkov Telescope, and the Very Energetic Radiation Imaging Telescope Array System have observed diffuse gamma-ray emission strongly correlated with the central molecular zone in the Galactic center. The most accepted scenario to generate this emission is via a hadronic interaction between cosmic rays (CRs) and ambient gas, where CRs are accelerated from a central and continuous source of 1 PeV protons. Aims. We explore the influence of the three-dimensional (3D) shape of the central molecular zone on the indirect observation of the CR energy density via gamma-ray detection. Methods. We simulated synthetic gamma-ray maps using a CR diffusion model with spherical injection, one isotropic diffusion coefficient, no advection, and mono-energetic particles of 1 PeV. Also, we used two different 3D gas distributions considering the observed gas column density, both with and without an inner cavity. Results. We find that when using a persistent CR source, a disk-like gas distribution is needed to reproduce the existing CR indirect observations. This is in agreement with the continuous gas distribution implied by some dynamical models and studies based on the comparison of emission and absorption molecular lines. However, it contradicts several models of the central molecular zone, which imply that this structure has a significant inner cavity. This tension can be reconciled by an additional, impulsive CR injection. Conclusions. If the central molecular zone has a cavity, a composite CR population, coming from the stellar winds of the Wolf-Rayet stars in the central 0.5 pc and the supernova Sgr A East, produces a good match to the observed gamma-ray morphology in the Galactic center.