No one ever could prove , not even remotely prove, that God was wrong or in error.
However, experience has shown that many, many people have been in error as to what God actually said in scripture. And that's where people mess up in interpreting the Ark story.
It is worth noting that the numbers included here are only initial estimates drawn from currently available information. On the other hand, a hypothetical 3D-digital ark created by the Ark Encounter design team, complete with all enclosures, interior structural elements, food, and water storage, showed that everything fit extremely well with little space left over.
Seems to me an easy way to test this. Build an ark, load it up with the required animals and people let it drift on the ocean for the requisite time without external aid.
That would settle everything. However, I doubt of that is going to be done, for reasons we all understand.
Depending on what cubit you use, the Ark would have had something a bit less than 2,000,000 cubic feet. If you packed every cubit with sheep, (stacked on top of each other) you could fit in maybe 120,000 sheep. But of course, you can't pile in sheep like lumber. So maybe a third of that. Say 40,000 sheeplike animals. But generally, you need about 35 cubic feed of silage for one sheep every year. (and someone will have to haul the feces of that topside and remove it pretty much every day)
You can, however, pack fodder like lumber, so for each sheep, you'd need about 35 square feet of deck space to store the food for one sheep. Assuming five decks on the Ark, (six cubits floor to ceiling) You get about 31,000 square feet of space. So if you store nothing but fodder on the Ark, you can store a years rations for about 886 sheep.
But then you'd have no room for the sheep themselves. Which is a linear programming problem. The simplex algorithm would give you the optimum use of space for sheep and fodder to get the most animals.
The simplex method uses an approach that is very efficient. It does not compute the value of the objective function at every point; instead, it begins with a corner point of the feasibility region …
math.libretexts.org
If you really want to see the numbers for that, I suppose I can set it up for you, but suffice to say it would be much less than 200 sheep.
Water would be another issue, given that the seas would be brackish at best. I suppose a really good rain collection system would work, although again, someone would have haul up urine topside to dispose of it. For a few hundred animals, it doesn't seem like an impossible task, but of course the Ark would have to keep thousands of animals with their required feed.
And since wooden vessels the size of an Ark will hog in even mild seas, and leak badly, someone will have to be manning the pumps pretty much 24/7.
As I said, these are reasons we will never see someone actually try doing a real-world test of the feasibility of an Ark.