500 million years have past since humanity came in control of a device that could send ships at great speeds across the universe, from the edge of one galaxy to the edge of another in weeks, sometimes even days. (There is a slight randomness of a couple of days to the travel time)
Problem 1 is the time frame of 500 million years that has already been pointed out. A civilization of 5000 to 10,000 years might be more digestible for a reader and easier to comprehend and understand why the Galactic Kingdom is now at WAR. Or why put any empahise on the timespan at all. Why not just a passing "We have been here for x number of eons and we are not going to let any c-- s---- b--- aliens with lizard popping green eyeballs just push us around." Humans can be prolific breeders with just enough spare time and resources.
Problem 2 is your device - somewhere you will have to explain its beginning and function. Calling it The Device and that it was found by the cave trekking Bob and Fred when eveyone thought they were lost but Eureka they came out 2 weeks later with The Device and told stries of going to other worlds leads nowhere but to rolling eyeballs. On second thought maybe that would work and they have statues in every world now..Surely every ship has The Device, in which case it has been duplicated and its internal workings known to the users. It is powered by the gamma phase inversion of space itself pioneered by Dr. Ginup D. Picjonston and Dr Emily Snod-Humfotjucot and allows a craft to create an expansion in space in the direction of travel with the ship being pulled along for the ride.
And as they say the rest is history.