I'd say our carriers are pretty safe as long as they stay out of range of the Chinese land-based short & med range ballistic missiles across the straights form Taiwan. Just too many of them SOBs. "Too many" as in "likely 10X more than our carrier group has anti-missile munitions." too many.
Then, there is the sort of attack that requires less tech and more brainpower. Asking questions like, "If we fight the Americans over <Taiwan, Japan, S Korea, whatever>, where would they deploy a carrier?" And then post weapon systems where they could range those locations.