Ah, but the bible says that it carried two of every kind. Implying that it’s not every single species, but instead 2 of every general type. Say, 2 large cats (potentially even just 2 cats in general covering small to large), 2 wolves, 2 bears, etc., but not 2 lions, 2 tigers, 2 lynx, 2 coyotes, 2 wolves, 2 domestic dogs, 2 sun bears, 2 grizzly bears, 2 black bears, 2 polar bears, etc.
As far as the size of the boat goes, it was to be 3000 cubits long, 50 cubits wide, and 30 cubits tall. If we assume a small cubit (it’s the length of the forearm) at 18 inches, that would give us a measurement of 450 feet long, 75 feet wide, and 45 feet tall. It’s further divided into 3 tiers or decks. If we assume that the floor separating each deck is ~1 foot thick, and each deck is the same height, we’d still have 472,500 cubic feet per floor or to give an idea of the floor space, 33,750 sq. feet. This gives a total of 101,250 sq. feet. One estimate I’ve seen for the number of land animals and birds that would have been on the ark (remember, 2 of each kind, not 2 of each individual species) was 16,000. If we ignore the differences in size between each animal and give each pair (8,000) the same amount of room, they’d have 12.65 sq. feet of room. Now remember, that’s if we gave rodents and elephants the same amount of floor space. If you’re smart about your space management for each pair of animals, you can manage to fit them all in with enough room. If you only take young animals that are either just entering sexual maturity or will enter sexual maturity shortly after getting off the ark (total time spent on the ark was roughly 1 year) they will tend to be smaller than full grown animals, especially concerning the animals that became very large.