Confining gauge theories are known to exhibit large-$N_c$ volume independence, i.e., finite volume effects from compactifying any space-time dimension are suppressed by factors of $1/N_c^2$. Compactifying the temporal dimension, this implies thermal effects are also suppressed. This feature breaks down if a deconfined phase is reached beyond a critical compactification radius. We explore the large-$N_c$ properties of confining gauge theories out of thermal equilibrium. We find analogous suppression of terms with factors of $1/N_c$ and $1/N_c^2$ within the confined phase, the first kind arising from far-from-equilibrium contributions. This suppression breaks down when deconfined states are accessed in the non-equilibrium time evolution, a feature that can be used to define non-equilibrium order parameters at large $N_c$. We show explicit results for a (1+1)-d integrable field theory after a quantum quench, where the non-equilibrium time evolution can be computed analytically, and $1/N_c$ suppression of terms is manifest.