Yes, if a civilization had the technology to travel close to the speed of light, they would still face significant challenges in traversing vast cosmic distances. The universe is indeed immensely vast, and even at relativistic speeds, it would take a considerable amount of time to travel to distant galaxies, let alone explore the entire universe.
One of the consequences of traveling near the speed of light is time dilation, as predicted by Einstein's theory of relativity. As an object approaches the speed of light, time slows down relative to an observer at rest. This means that for the travelers themselves, the perceived duration of their journey might be relatively short. However, from the perspective of observers outside the spacecraft or those remaining on their home planet, significant amounts of time would pass.
The distances between galaxies are immense, and even traveling at near-light speeds, it would take an enormous amount of time to reach them. Additionally, as an object accelerates to such speeds, it requires increasing amounts of energy, which poses its own challenges.
Moreover, the expansion of the universe adds another layer of complexity. The space between galaxies is expanding, causing them to move away from each other at an accelerating rate. This expansion further complicates long-distance travel, as the cosmic distances between galaxies are expanding faster than one could potentially traverse them.
In summary, while traveling close to the speed of light would provide some benefits in terms of time dilation for the travelers themselves, the vastness of the universe and the challenges posed by cosmic distances and the expansion of space would still present significant hurdles to fully exploring the universe, even with advanced technology.