I just realised that because of the conservation of energy law (energy cannot be created or destroyed), the cooling of the universe must translate into something.
When things in our day to day life go through the process of cooling, it’s different. In those cases the heat energy is passed from one place to the next.
Matter is energy, and energy is matter. The universe is all that is, and all places that are. Because the universe is the “mother” system, energy cannot be passed to “another place”. Because of this, the very fact that the universe is cooling would have to lead to the spontaneous creation of matter in some way, because the energy has nowhere else to go.
(I may be missing something here. If so please correct me :))