Update:
After disastrous attempts to steal the Giant Elephants, thwarted by combats such as "clashes with 18 giant elephants", I decided I needed a better strategy.
So I embarked right next to the Elf Forest Retreat which sends the caravans, and the elves had obviously clear-cut the forests around their "forest retreat" as all the trees were missing, with suspicious patches of sand which tend to be left when cutting down a tree. There were some elves living in the area. I trapped the elves and imprisoned them for their crimes against the forest (I'd have set a quota, but since they'd already cut the trees down it wouldn't do any good).
I then built up the fortress and started raiding. I figured that sending a bunch of raids not to steal but just look around would be good, and trained up ambusher some.
Then I started stealing livestock, and it got hilarious.
I have so far failed to steal a giant elephant, but I have stolen hundreds of animals, including many giant animals some of which are war-trainable. I'll send in about 25 dwarves at a time, and bring back about that many animals. I feel like animal control dealing with a crazy cat lady cat hoarder, if I'm not to become the crazy cat lady I'm going to have to start dumping the less valuable animals into magma. The animals are of course extremely happy to have been liberated from the inhumane conditions the elves keep them, so it would be sad to toss them down the magma shaft, buuut FPS.
My dwarves meet the Giant Elephants during the raids sometimes, so they're definitely there. They just can't or wont steal any.