Not unless a lot of what we currently believe turns out to be false. The theory of special relativity tells us that it is impossible for anything with more mass than a proton to travel at light speed. But if we can’t even reach light speed, then there’s no way we could surpass it. Furthermore, it isn’t some fringe corollary to the theory that tells us this. It directly follows from the central equations (i.e. E=mc²), so the theory would have to be wrong on a fundamental level for warp speed to be achievable. But even if Einstein was massively mistaken and we can create bubbles in space-time to travel through, it may yet be impossible to have faster-than-light spacecrafts. For one, the amount of energy we would need to propel an object at warp speed would be so large that we’d be converting entire planets into fuel just to get the process started. For another, the bubble would probably be prone to collapsing in on itself. And finally, anything inside the bubble would probably be subjected to Hawking radiation at a temperature of 10³⁰K. So it’s probably impossible. And even if it’s not, we’d be using a lot of resources to create something that would probably burn us to death (assuming we weren’t crushed first by space-time itself).