In theories beyond the Standard Model of particle physics, the new particles in the so-called dark sector can have large lifetimes, commonly referred to as long-lived particles (LLPs). We motivate the quest for new, long-lived physics at colliders able to explain dark matter. The impact of the cosmic reheating dynamics on dark matter freeze-in production will also be discussed in a specific Higgs-portal model. The crucial role of collider LLP searches is emphasized, focusing on prospects at the Future Circular Collider (FCC-hh), to unveil new dark sector physics.