Abstract We demonstrate optical cycling and laser cooling of a cryogenic buffer-gas beam of calcium monohydride (CaH) molecules. We measure vibrational branching ratios for laser cooling transitions for both excited electronic states A and B . Furthermore, we measure that repeated photon scattering via the A ← X transition is achievable at a rate of ∼ 1.6 × 1 0 6 photons s −1 and demonstrate interaction-time limited scattering of ∼ 200 photons by repumping the largest vibrational decay channel. We also demonstrate a sub-Doppler cooling technique, namely the magnetically assisted Sisyphus effect, and use it to cool the transverse temperature of a molecular beam of CaH. Using a standing wave of light, we lower the transverse temperature from 12.2(1.2) mK to 5.7(1.1) mK. We compare these results to a model that uses optical Bloch equations and Monte Carlo simulations of the molecular beam trajectories. This work establishes a clear pathway for creating a magneto-optical trap (MOT) of CaH molecules. Such a MOT could serve as a starting point for production of ultracold hydrogen gas via dissociation of a trapped CaH cloud.