What would be the best way for Bitcoin and alts to protect themselves against this threat when it is on the verge of being created?
post-quantum cryptography
like lamport signatures already exists, and it could be implemented into bitcoin today. that's the easy part.
the difficult part is dealing with the 5+ million vulnerable coins (p2pk outputs, outputs sitting in reused addresses, shared xpubs, etc). implementing a post-quantum signature scheme alone doesn't address the fact that 1/3 of the supply is vulnerable to theft. people need to voluntarily move their coins to quantum-safe addresses for the fork to be effective. that could take a few years, based on the adoption rate of segwit.