We present a first-principles method to calculate electron-phonon coupling elements in atomic systems, and showcase its application to the evaluation of the phonon-limited mobility of n-type single-layer MoS₂. The method combines a density functional theory (DFT) plane-wave supercell approach with a real-space maximally localized Wannier basis. It enables the calculation of electronic structure, phonon displacements with their corresponding frequencies, and real-space electron-phonon coupling elements on the same footing, without the need for density functional perturbation theory (DFPT) or Wannier interpolation. We report a low-field, intrinsic mobility of 274 cm²/Vs at room temperature for MoS₂, and highlight its dependence on carrier density and temperature. In addition, we compare our findings to the latest available modeling data and put them in perspective with the experimentally measured values. Based on these observations, the mobilities presented in this work appear to be compatible with experimental results, when taking into account other scattering sources. Hence, the proposed approach provides a reliable framework for mobility calculations that can be extended towards large-scale device simulations.