According to our current understanding of physics, it is not possible for spaceships or any other massive objects to travel faster than the speed of light in a vacuum. Special relativity, which is a well-tested and widely accepted theory, prohibits the motion of massive objects at or beyond the speed of light.
As an object with mass approaches the speed of light, its relativistic mass increases, and time dilation effects become significant. The closer an object gets to the speed of light, the more time dilation it experiences. However, as an object with mass reaches the speed of light, its relativistic mass would become infinite, which is not physically possible.
There are various speculative concepts and theories that involve faster-than-light travel, such as wormholes and Alcubierre drives. However, these ideas are purely hypothetical at this point, and there are significant theoretical and practical challenges associated with them.
It's worth noting that our current scientific understanding is subject to change as new evidence and theories emerge. However, as of now, faster-than-light travel for massive objects without time dilation remains firmly outside the realm of known physics.