We point out a surprising consequence of the usually assumed initial conditions for cosmological perturbations. Namely, a spectrum of Gaussian, linear, adiabatic, scalar, growing mode perturbations not only creates acoustic oscillations of the kind observed on very large scales today, it also leads to the production of shocks in the radiation fluid of the very early Universe. Shocks cause departures from local thermal equilibrium as well as create vorticity and gravitational waves. For a scale-invariant spectrum and standard model physics, shocks form for temperatures 1 GeV<T<10^{7} GeV. For more general power spectra, such as have been invoked to form primordial black holes, shock formation and the consequent gravitational wave emission provide a signal detectable by current and planned gravitational wave experiments, allowing them to strongly constrain conditions present in the primordial Universe as early as 10^{-30} sec after the big bang.