[NoMoreNicksLeft]

It's quite simple really. All we need is fast-as-light technology.

If you get in a ship and travel to Alpha Centauri at the speed of light, the travel seems instantaneous to you. But the people you leave behind think you've been gone 8 years when you return.

So instead, I propose that when the ship launches, we also propel the rest of the universe in the opposite direction also at the speed of light. Then, when the astronaut is scheduled to return, we propel the entire universe at the speed of light back to its original location.

All of reality undergoes time dilation. And the trip is basically instantaneous for all involved†.

† Note: This form of FTL is mildly costly in regards to energy expenditure.