Often it's said that Relativity doesn't allow any information to travel faster than the speed of light.
That's exaggerate and not true.
It's been shown that quantum entanglement allows information to travel faster than the speed of light. If a system is entangled, meaning it's a superposition of two states, when an interaction causes the system to fall into one of those two states, that happens instantly everywhere irrespective of how big the system is.
So, for example, if two photons get entangled and then one of them is sent to a nearby galaxy, afterwards the system comprising the two photons stretches from our galaxy to the nearby one, and, irrespective of that, an interaction with the local photon can cause an instant change in the distant one located in the another galaxy.
So information can move instantly whatever the distance.
I think, but I'm not going to prove it, that the limitation due to the speed of light regards only energy and momentum, not information.
That is not surprising, because it can be shown that the fact the laws of physics are the same everywhere causes energy and momentum to be conserved during the evolution of a system. So energy and momentum are deeply connected with the structure and geometry of spacetime, in a way that their transfer is subject to the geometrical laws of spacetime (of which the speed of light is just an aspect).
Information instead, and who knows what else, can move instantly.
In the above example, sending the photon to the nearby galaxy is a transfer of energy, that's why it's subject to the speed of light limit. But once energy is in place, that limit doesn't apply to information transfer.
So, if I may end on a sci-fi note, one may imagine harvesting photons entangled from the beginning of the universe to send information instantly to every corner of it.