[lmm]

There's no proof that it's the only possible way - but no-one's ever been able to come up with a concrete alternative.

[Orlanthai]

There are other alternatives such as the derivation of quantum theory within the GPT framework and many other axiomatic derivations.

I've never seen the Born rule derived from unitary evolution and axioms for how subjective experience should work, so I don't even see this as one of the ways.