To sum up the conclusion of the several-hour video series: the Aegis Combat System is essentially impenetrable to all but the most overwhelming of forces.
Perhaps not, but missile cruisers can :) They try that in a different series, a fully armed WWII battleship group against a modern US carrier group. Guns just don't have the range compared to surface launched missiles and they can't get close enough.
I won't pretend to be some expert on military hardware, I'm a guy interested in flight sims, and that video series just happened to catch my attention. They make a compelling argument though, cruise missiles are one of the methods they try (unsure if supersonic), and they are attacking the carrier group in the absolute worst defensive position it could be in: a narrow gulf surrounded by unfriendly territory on most sides.
Still, not much gets through. If it's not the missile defense system that gets you, it's the F/A-18 patrols. If not them, it's the F-14s that can scramble in minutes. Scary stuff.
https://www.youtube.com/watch?v=1K8LGTwy6Zw
To sum up the conclusion of the several-hour video series: the Aegis Combat System is essentially impenetrable to all but the most overwhelming of forces.