Supernovae occurring in dense winds are promising candidates for particle acceleration to high energies. We focus here on the onset of particle acceleration, during the first couple of days following core-collapse. We show that a collisionless shock rapidly forms at supernova shock breakout. We calculate the CR energy that can be reached in such environments. We take the effect of cosmic-ray energy losses due to inelastic $pp$ and $p\gamma$ collisions into account, as well as possible damping of the turbulence by radiation. We find that protons are accelerated to multi-TeV energies within minutes to hours for Wolf-Rayet and red supergiant progenitors. Secondary high-energy neutrinos with energies greater than $\sim 100$ GeV are expected to be produced.