I should probably have titled this "Ark Challenge", since that is essentially what it is.
I think that if Thor Heyerdahl can slap together a primitive Polynesian-style raft and cross the Pacific ocean, surely someone could at least prove that "Noah's Ark" could have been possible.
I would even make my requirements as easy as possible! Since the test is mostly one of seaworthiness and keeping some animals alive, I would forgive them modern manufacturing techniques and the requirement to preserve all land-based life from a global flood.
What I would require would be that the Ark be built in such a way that it matches as much biblical description as possible and could have been built using "contemporary" (ca. 2000 BCE) techniques. I don't care if they use power tools and CNC machines to make the parts, a long as the result could have been achieved back then. I don't care if it is built in a modern dry dock, as long as an ancient method could have succeeded. I expect them to justify their dimensions and material use according to their choice of translation/version of biblical descriptions of the Ark.
On board, again, I will cut them plenty of slack. Since the marsupials of Australia were unknown to the ancient Hebrews, we can pretend that God made them after the flood, to deal with an unpopulated continent. The same goes for any indigenous life of the Americas. I do, however, expect them to carry aboard all known land animals mentioned in the Bible, in pairs or sevens as appropriate. This would probably include all common domesticated animals, and a few wild ones. Since the flood myth does not mention Noah keeping the plants or freshwater fish alive, I'll even give them a supernatural "bye" on those.
In a nutshell, the challenge becomes for them to go to sea for the appropriate amount of time (as justified by their choice of biblical interpretation) in this boat, and then be able to land and set up a functioning farm (and they can do this wherever they like - a place with great soil, water supply, etc. is fine) with only the supplies and creatures they still have on board.