We still can't explain the big bang, yet here we are. Just because something can't be explained with our current models or understanding, doesn't mean it's forever impossible.
what we cannot explain must still obey the rules we have figured out. Much as you might wish otherwise.
I have one thought on FTL travel. Creation of a “naked singularity” by spinning a black hole fast enough to counter the forces holding it together. However the singularity will remain incompatible with our universe, and will then spread at the speed of causality popping, destroying everything in its path. But within that new universe, it might be possible.