In order to accommodate the QCD axion as the dark matter (DM) in a model in which the Peccei-Quinn (PQ) symmetry is broken before the end of inflation, a relatively low scale of inflation has to be invoked in order to avoid bounds from DM isocurvature fluctuations, H-* less than or similar to O(10(9)) GeV. We construct a simple model in which the Standard Model Higgs field is non-minimally coupled to Palatini gravity and acts as the inflaton, leading to a scale of inflation H-* similar to 10(8) GeV. When the energy scale at which the PQ symmetry breaks is much larger than the scale of inflation, we find that in this scenario the required axion mass for which the axion constitutes all DM is m(0) less than or similar to 0.05 mu eV for a quartic Higgs self-coupling lambda phi= 0.1, which correspond to the PQ breaking scale v(sigma) greater than or similar to 10(14) GeV and tensor-to-scalar ratio r similar to 10(-12). Future experiments sensitive to the relevant QCD axion mass scale can therefore shed light on the physics of the Universe before the end of inflation.