After developing some intuition for relativity you realize that asking whether FTL is possible is more akin to asking whether you can remain inside a circle after traveling radius + 1 from the center, than it is to asking whether a car can be modded to exceed its top speed. It is nonsensical, not logically coherent within all currently known physics and it goes to the fundamental nature of motion itself.

It can't be ruled out, but neither can Russell's Teapot.