Wherever it came from.
He fed them unicorns.
How did those cute little koala bears get to and from Australia without getting eaten and without any Eucalyptus trees along the way for food? Or did the "flood" not reach Australia, North and South America, Antarctica? Not to mention anywhere in Asia, Europe, Africa, or anywhere else detectable.
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
*Noe also had Hoodia Trees on board
I obviously don't know the answers since I wasn't there and the Bible doesn't provide the details. Proposals that I've heard that make the most sense are:
Where did all the water go after the flood?
Prior to the Flood the Earth had a fairly mild terrain without high mountains and deep sea trenches. During/After the Flood - when "...all the fountains of the great deep broken up, and the windows of heaven were opened" - mountain peaks rose up, and sea trenches were created in the oceans beds -- thus allowing a recepticle for the water that covered the surface of the Earth.
What did Noah feed to the lions and tigers during his voyage? As I understand it both have hearty appetites.
One proposal is that most of the animals went into 'hibernate mode'... I know if I had been on board the last ship on Earth, while 'terra firma' was getting ripped up and covered with water I'd probably been in a 'wake me when its over mode' as well...
God Bless.