Well, Noah's ark is testable, isn't it, at least as testable as, say, the story of the Trojan horse? While one could never prove that there had never been a big boat at that time, one could find evidence that there was such a thing.
I can imagine what such a find might look like. Remember those silly documentaries from the 1970s showing fuzzy photographs of the ruins of the "ark" amongst the rocks of Mt. Ararat? Not exposed to the wind and weather like that, but perhaps one could find buried remains of a huge boat. With dendrochronology we would have a shot of dating the find down to the exact year. If it were accompanied by written records mentioning Noah and lists of "kinds", remains of foodstuffs, etc., it might be a slam dunk - at least for some elements of the ark story.
I have seen several of those TV shows that talk about the remains of Noah's Ark being found on Mt Ararat. But somehow, they can never get the conclusive evidence that the Ark is really there. The weather is bad, the political situation is bad, there is always a problem. I think that if the Ark where really up there they would have found it by now. It's just a big BS story.
Ebal Trace