Is not the point that it is only material objects that cannot exceed c?
Information can. Is that not correct?
Currently, information can be transmitted only by some transmitting medium. The fast medium currently known is light, and no, light cannot exceed the speed of light.
Material objects can be viewed as a kind of frozen light. That isn't actually accurate, but it is close enough for a rough approximation.
If we model an atom as some assembly of photons bound together such that they orbit some center, then as the atom is accelerated, the orbit will happen slower in the direction of travel and so will appear to an outside observer to be slowing down.
This is what is observed to happen to material objects.
This might make for some understanding why nothing material can travel faster than light, or even actually reaching light speed.
Ther is hope for FTl (Faster Than Light travel) however. It seems that space and time are not really independent entities. Spacetime can be warped. We see this warping about massive objects. The Sun can paradoxically magnify objects beyond it in certain circumstances. We have been able to detect the warping of space. That's how the 'Gravitational Telescopes work.
There are some ideas on how we might be able to use this warping ourselves. Currently we know only a handful of ways to warp space. None of them are usable for travel, but the mathematics says that it is possible to so warp space that an object contained in a bubble of warped space can appear to move faster than light because the distance is so reduced.
In extreme cases, you might have a "Stargate" that brings the distance between you and another planet about another star only a short walk away. Such a thing is possible, but not likely to be survivable by any means we now can envision.
So yes, it's possible, but no, we have no idea how to do such a thing.
It's rather like trying to design a boat to exceed the speed of sound for the ancient Greeks. Just how many rowers must your Trireme have to row faster than sound travels?What sort of wood is best used for it's construction?
It's (exceeding the speed of sound) now been done, but we didn't use triremes, nor did better designed oars help at all.
When we talk of starships, we are just like those Greeks, using Triremes when something totally different is needed.
For FTL Starships, we don't know the answers and we probably don't even know the questions.