Breaking the speed of light barrier is impossible. As one travels faster and faster, one's mass increases. At the speed of light, one's mass becomes infinite and would require infinite power to achieve.

This is why the photon is the only particle that can travel at the speed of light because it has no mass.

Star Trek is a fictional story. The writers of that series know that the speed of light is a barrier that they cannot breach. But, what if we could break that barrier? Then, we could travel the vast distances to reach far away planets. If we do not allow the story to break the speed of light barrier, we do not get Star Trek. So, this story is only possible in fiction by assuming the speed of light barrier is broken, which it cannot be.

Aliens also cannot break the speed of light barrier. This is why we do not see aliens on earth.