According to our current understanding of physics, the expansion of space during the Big Bang did not involve objects within space moving faster than the speed of light. The concept of "space traveling faster than the speed of light" is not supported by the theory of general relativity.
However, if we consider a hypothetical scenario where an intelligent civilization exists on a planet that somehow travels faster than the speed of light, we can speculate on the possible consequences.
According to Einstein's theory of relativity, as an object with mass approaches the speed of light, its energy and momentum increase dramatically, and its perception of time slows down relative to an observer at rest. This phenomenon is known as time dilation.
If the civilization were to travel at speeds approaching or exceeding the speed of light, they would likely experience significant time dilation effects. Time would appear to pass more slowly for them compared to an observer on a stationary planet. For example, if they traveled near the speed of light for a certain period, they might age much less compared to someone who remained on a stationary planet.
This time dilation effect has been experimentally confirmed for objects traveling at high speeds relative to each other. However, surpassing the speed of light is currently considered impossible according to our current understanding of physics, so it is purely a hypothetical scenario.
It's important to note that our understanding of physics is based on our observations and experiments within our own universe. Speculating about the consequences of surpassing the speed of light or the nature of other hypothetical universes is still a topic of ongoing scientific research and exploration.