I want to make my world as realistic as possible, so no otherworldly FTL ideas like wormholes, teleportation or warp/alcubierre drives that will violate causality according to relativity. Let's begin.
Near a black hole, the gravitational time dilation can make spending a year there equal a million years in the outside universe. From your point of view, everything near you behaves normally, the clock ticks by at one second per second, light travels at 299,792,458 m/s etc. But you will see a clock in the outside universe tick a million times faster. Time of the outside universe runs a million times faster from your POV, and that subsequently includes light itself. Well, light still travels at 299,792,458 m/s, but since s is much shorter, it'll appear much faster. Light from the Andromeda Galaxy only took 2.5 years of YOUR time to reach you. Conversely, someone viewing you from the outside universe will also experience normal time and speed of light, but they'll see your clock tick one million times slower.
We've observed this effect back in 2015, where we PREDICTED a supernova down to the month. And it actually happened in December that year. Well, kinda. That very same supernova was seen in 2014. It came to earth in six different images due to the light being lensed by a massive galaxy cluster in front of it. Light passing near massive objects will appear slower to an external observer. That's why the one image that passed through the least gravitational disturbance, came to Earth first, in 1998. The next four images reached us in 2014 within 3 weeks of each other, then the last one in December 2015, just as predicted a few months earlier.
Now to the juicy part, is it possible to make a field with the opposite effect? One where observing from the outside universe makes everything inside the field appear a million times faster, and vice versa for an observer inside the field. One million years inside the bubble equals one year outside. Suppose now whatever you've made this field with, you somehow stretch it all the way to the Andromeda Galaxy. This is obviously gonna take many millions of years so assume someone has already done it for you millions of years ago. Bam! Now you have an interstellar superhighway, one billion kilometers in cross section, stretching all the way from our solar system to Andromeda. As you enter this tiny strip of distorted spacetime with your spaceship, you'll gradually see the outside universe redshift out of view and their clocks tick slower and slower.
You've finally reached your desired point. Here, your time is ticking a million times faster than outside. Now what? The Andromeda Galaxy is still 2.5 million light years away and it still takes 2.5 million years to reach it with lightspeed. "It's just gonna APPEAR much faster from the outside when I'll be long dead in my spaceship, such a stupid idea!" you might think, but what if I told you, you can use another trick in the book? Let me introduce: Special Relativity! You accelerate to 99.99999999995% of the speed of light, that's an impressive 0.15 mm/s slower than light itself! At that velocity, your Lorentz factor is one million, so your trip to Andromeda is a million times shorter. You decelerate at the end of your journey, 2.5 years later from your perspective. 2.5 million years would still have passed inside the bubble, which means only 2.5 years has passed in the outside universe. Now wait a second...
Did you just hack the universe? Would it even be possible to create such a contraption? Would it violate causality? Why or why not?