That all said, none of this is impossible, and first tier militaries are putting a whole lot of effort into this problem; in a sense, "it's just engineering." But so far no first tier military has actually seen how their system would work in the field, and the results remain to be seen.
Particularly, if China were sure that it could sink American carriers at will, it would already be invading Taiwan.
The US Navy is actually pretty good at avoiding that.
https://www.globalsecurity.org/military/library/policy/navy/...
It's much harder than it sounds.
A ballistic hypersonic missile isn't like a TV-guided cruise missile that can track a moving target or a HARM that will seek out RF signatures. You'd basically have to wait until the carrier is parked somewhere for an expended period (multiple hours at a minimum), otherwise you'll waste a $100M hypersonic missile.