Soon after the MAVEN (Mars Atmosphere and Volatile EvolutioN) spacecraft started orbiting Mars, the SEP (Solar Energetic Particle), SWIA (Solar Wind Ion Analyzer), and STATIC (Supra‐Thermal and Thermal Ion Composition) instruments on board the spacecraft detected planetary pickup ions. SEP can measure energetic (>60 keV) oxygen pickup ions, the source of which is the extended hot oxygen exosphere of Mars. Model results show that these pickup ions originate from tens of Martian radii upstream of Mars and are energized by the solar wind motional electric field as they gyrate back toward Mars. SWIA and STATIC can detect both pickup oxygen and pickup hydrogen with energies below ~30 keV and created closer to Mars. In this study, data from the SEP, SWIA, and STATIC instruments containing pickup ion signatures are provided and model‐data comparisons are shown. During the times when MAVEN is outside the Martian bow shock and in the upstream undisturbed solar wind, the solar wind velocity measured by SWIA and the solar wind (or interplanetary) magnetic field measured by the MAG (magnetometer) instrument can be used to model pickup oxygen and hydrogen fluxes. By comparing measured pickup ion fluxes with model results, the Martian thermal hydrogen and hot oxygen neutral densities can be probed outside the bow shock, providing a helpful tool in constraining estimates of neutral oxygen and hydrogen escape rates. Our analysis reveals an order of magnitude density change with Mars season in the hydrogen exosphere, whereas the hot oxygen exosphere was found to remain steadier.