The direct detection of dark matter particles with mass below the GeV scale is hampered by soft nuclear recoil energies and finite detector thresholds. For a given maximum relative velocity, the kinematics of elastic dark matter nucleus scattering sets a principal limit on detectability. Here, we propose to bypass the kinematic limitations by considering the inelastic channel of photon emission from bremsstrahlung in the nuclear recoil. Our proposed method allows us to set the first limits on dark matter below 500 MeV in the plane of dark matter mass and cross section with nucleons. In situations where a dark-matter-electron coupling is suppressed, bremsstrahlung may constitute the only path to probe low-mass dark matter awaiting new detector technologies with lowered recoil energy thresholds.