Pyramids are possible, we have proof that they are. The ark, we have no proof of any structure that large and it would have been preserved and talked about in contemporary history until it was totally rotted away. If anything something that immense, would be like the pyramids, revered, imitated and documented at least until the Greeks/Romans.
Same goes for the Tower of Babel soon after, if they were halfway done as the Bible says and then suddenly dispersed, where are the ruins? There is more "evidence" of King David or King Solomon (which also never existed in contemporary history and retconned a local warlord into Jewish lore) than the ark.
Besides the obvious engineering issues, why did God need a physical device at all? He could just put them all on a "unusual high mountain" like Satan did to Jesus or even just China, which has a continuous written history through the flood time or just wiped the people out without all the rain (which a mass flood can't be found in the geological records)