Wouldn’t it be great to travel at Warp speed?
The answer to your question, surprisingly enough, is not necessarily “No, humans will never invent a way to travel through space fast enough to reach far away galaxies.”
Here’s the deal. The faster you go, the slower you age, so if you could go almost the speed of light, then it would still take you millions or billions of years to fly to other galaxies from Earth’s point of view, but not so for you who are traveling in the spacecraft. For you the time would be dilated.
Look at an example introduced by Albert Einstein. Consider two twins, named Biff and Cliff. On their 20th birthday, Biff decides to get in a spaceship and take off into outer space, traveling at nearly the speed of light.
He journeys around the cosmos at this speed for about 5 years, returning to the Earth when he is 25 years old.
Cliff, on the other hand, remains on the Earth. When Biff returns, it turns out that Cliff is 95 years old.
Similarly, Biff could travel to other stars and galaxies if he could somehow go fast enough, but meanwhile whole civilizations, humanity and even Earth itself would grow old and cease to exist. So when Biff gets there, Cliff will be long gone. Biff will have traveled forward in time as his spaceship zipped through the cosmos.