TFC: That may be true, but that science is based on our rudimentary understanding of matter in our universe. Relativity is an excellent explanation for the motion of large objects, however, we do know that its rules breakdown at quantum levels. Action at a distance is possible within quantum theory, which predicts that information can travel faster than light as well as out of temporal sequence (i.e. a future event affecting a result in the present.) Attempting to navigate the universe by shifting galaxies around may not be the most pragmatic approach to interstellar travel. With quantum mechanics you can conceivably access pre-established connections between all points in the universe and instead of physically transporting a human observer, you simply manifest the observer into a new environment, thus leapfrogging the supposed lightspeed restriction.
This fundamental manipulation of matter may bring us the dream of replicators able to construct objects on the fly, access fleeting moments in the timeline and alter our bodies like changing a TV channel. This technology may not leave a "trail" of any sort. In fact a user may not even need to leave his or her bedroom to explore Zeta Reticulii! So expecting an alien civilization to leave footprints according to our clunky baseline might be a tad bit naive.
Additionally Forever 21 makes a good point. We do not know how many universes rose and fell before ours or how many co-exist with ours at this moment in time. Within all of this potential an alien civilization might have developed a way to escape their universe and enter others, maybe even by breaking the lightspeed barrier. All it takes is one to set a precedent. Whether or not they would want to share this tech is another matter.
Whoho... our understanding of the universe is of course clearly not perfect but I would not exactly call it rudimentary. True we do not have a complete unified theory of relativity+quantum theory, but some aspects hold even here. Quantum tunneling is the only process I can think of that truely allows travel of particles "faster than light" (the term is not really applicable in this context, though). You are reffering appearently to quantum entanglement, but under no circumstance information can be transmitted/exctracted using this phenomenon (the wikipedia article should explain this).
I never heard about the future affecting the present or from its perspective the past - could you be more specific about this? And what pre established connections are you talking about? Leapfrogging light speed? Are you still talking about quantum entanglement? Those things are proven to be impossible within those frames. This is true even in a thought experiment maintaining a quantum entanglement while transporting the particles to the other side of the galaxy - and due to rapid decoherence wrt to the entangeld particles (another fundamental phenomenon of quantum mechanics) not even this is possible.
Star Trek quantum replicators are simple BS simply due to Heisenberg uncertainty. Apart from virtual reality simulations you will have to leave earth, doing long journeys taking thousands, millions, and billions of years or an unreachable amount of time - depending on the destination choosen.
Maybe there are other universes with other laws of physics. But this still does not enable anyone to break lightspeed in ours. Therefore, as far as can be told from the physics at hand, mankind is limited to our corner of the galaxy for any forseeable future - say the next 7000 years assuming that we invent near lightspeed drives any time soon. Otherwise it can take much longer.