  We explore the phase transitions at the onset of time-crystalline order in
$O(N)$ models driven out-of-equilibrium. The spontaneous breaking of time
translation symmetry and its Goldstone mode are captured by an effective
description with $O(N)\times SO(2)$ symmetry. Using the renormalization group
and the $\epsilon=4-d$ expansion in a leading two-loop analysis, we identify a
new non-equilibrium universality class. Strikingly, it controls the
long-distance physics no matter how small the microscopic breaking of
equilibrium conditions is. The $O(N=2)\times SO(2)$ symmetry group is realized
for magnon condensation in pumped yttirum iron garnet (YIG) films and in
exciton-polariton systems with a polarization degree of freedom.
