If it cannot in principle be measured or observed (with past, existing or future technology) then it cannot be true.
You seem to have "true" confused with "provable". There are uncountably infinitely many true things that can never be proven with any finite or countably infinite amount of time or evidence (proved via Gödel). There either is a god or there isn't: one of those must be true, even if we never know which.
Nothing is faster than the speed of light ... To prove this to yourself, try opening the refrigerator door before the light comes on.