Your example just serves to further strengthen my argument. The lack of experimental evidence for FTL travel is an astonishingly good argument that it doesn’t exist.
You should research the logical fallacy “argument from ignorance” which implies that a thing is true simply because it hasn’t been disproven to be true. That kind of argument is a feeble attempt to shift the burden of proof to the other party, when instead the maker of the claim is responsible to provide evidence for that claim.