In the context of Self-Interacting Dark Matter as a solution for the small-scale structure problems, we consider the possibility that Dark Matter could have been produced without being in thermal equilibrium with the Standard Model bath. We discuss one by one the following various dark matter production regimes of this kind: freeze-in, reannihilation and dark freeze-out. We exemplify how these mechanisms work in the context of the particularly simple Hidden Vector Dark Matter model. In contrast to scenarios where there is thermal equilibrium with the Standard Model bath, we find two regimes which can easily satisfy all the laboratory and cosmological constraints. These are dark freeze-out with 3-to-2 annihilations and freeze-in via a light mediator. In the first regime, different temperatures in the visible and the Dark Matter sectors allow us to avoid the constraints coming from cosmic structure formation as well as the use of non-perturbative couplings to reproduce the observed relic density. For the second regime, different couplings are responsible for Dark Matter relic density and self-interactions, permitting to surpass BBN, X-ray, CMB and direct detection constraints.