The Bush Family Posing on an Elephant in 1964
The original caption says it's a statue. But it fooled me long enough to start searching for other pictures of future presidents posing with extra large animals. Unless someone has a good pic of young Grover Cleveland with a rhinoceros, I guess I'll shelve the idea.
[Update: Reader Philip has found another posing-with-elephant photo. If that's the same one, that's one malleable statue.]
Here's the description from the George Bush Presidential Library and Museum:
The Bush family poses on an elephant statue during the 1964 Senate campaign. Left to right: Barbara, Doro, Marvin, Neil, Jeb, and George H.W. Bush (George W. was away at school).