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I don't think that we currently know enough about physics to say for sure that faster than light travel is impossible.
I think it's likely that there are still scientific breakthroughs to be discovered that will make currently impossible things possible.
You might be misunderstanding the problem, though. "Traveling" is relative. It absolutely is not impossible to arrive somewhere faster than light traveling in "normal" 3D space would. For example, 3D space itself is a medium, not an absolute thing. A medium can always be manipulated.
It also depends on how you are measuring time. From the perspective of the light, all travel is nearly instantaneous. It's only from our perspective that it appears to take a long time.
From the perspective of the light, wouldn't travel take a long time?
For everyone else, yes, but for you, no. The faster you go, the more time dilation affects your own experience of time. If you were to travel 1 light year at the speed of light, it would be instantaneous for you, but a year would pass for everyone on Earth.
We haven't seen anything in nature violate it nor in any lab.