It's probable that instead of mature large animals that Noah took younger animals.
It's also possible that Noah might have only had one pair of "Cat" on board from which several large cats including Tigers and Lions descended.
And if you believe that "God brought the animals to Noah", instead of Noah scurrying around collecting animals. Then it's also possible that God caused the animals to go into some form of hibernation.
For a picture of lion cubs nursing at a mother sow, see the following. Lions and Pigs lie down together
It's magic, magic!
Well, hell, why do you even need a boat then? Why not float them on a cloud and rain beer down on them?
Oh, wait, make that a beer volcano! Ramen!
What about Helen Thomas? Did Noah load her on board or did Helen sneak on board the Ark.
Danny. In all seriousness, there is just no evidence for a world wide flood, no matter how much you try to stretch or twist the evidence.
Ever think that the flood story is a lesson that was not to be taken as a literal event?
I suppose its also possible that God miniaturized all the animals and temporarily turned them into little ceramic figurines, and that Noah then stored them in hundreds of knick-knack cupbords for the duration of the trip.