Can that be proven? No, of course not. Science does not deal with proof.
But it can be said with certainty that it does make a sound.
Tests can be run. The hypothesis is that when a tree falls it makes a sound.
Run the test X number of times and record results.
Other scientists can replicate the tests. They do and sure enough, a falling tree makes a sound.
Soon you have a body of evidence that falling trees make sounds.
As always, Science holds it's conclusions tentatively. So if someone can prove that a tree can fall without making a sound, and that finding can be independantly confirmed, then it's back to the drawing board.
It's the heart of the Scientific Method.
A more dificult question, and one for you to ponder is:
If a man speaks in the woods, and no one hears him, is he still wrong?
Aslan is not a Tame Lion