Core-collapse supernovae exploding in dense winds are favorable sites for cosmic-ray (CR) acceleration to very high energies. We present our CR-radiation-hydrodynamics simulations of the explosion of a red supergiant. We study the evolution of the shock wave during the first day following core collapse, and estimate the time at which CR acceleration can start. We then calculate the maximum CR energy at the forward shock as a function of time, and show that it may already exceed 100 TeV only a few hours after shock breakout from the surface of the star.