It's probably more likely that we could colonize Mars before we will have a vessel capable of compressing space and traveling through it in an efficient manner.
For the latter, every astronaut in orbit is a time traveler since they are moving at such great speeds that they experience tie dilation. I believe the Juno spacecraft is the current record holder of time travel since it is the fastest man-made object.
I'm not that smart, but I have my doubts about light being the universal speed limit. Baseless rant incoming:
I never advanced that far in math, but I found the notion of infinitesimal limits and infinities hard to accept and they are most likely beyond observation if they do indeed exist. So I find the idea that it takes an infinite amount of energy to move a massive object at the speed of light to be a signal that perhaps although it is exceedingly accurate, that E=mc^2 doesn't quite tell the whole story. Waxing philosophical::
There are things that are certainly impossible according to the law of physics as we know it, such as FTL travel or time travel.
There is nothing according to the laws of physics that prevent us, say, from colonizing Mars.