Okay that is the relevant part of your post which I will comment on.
What is the maximum detection range of Indian AWACS, I consider it 400KM-500KM, and that is for an aircraft flying within the area. If 10 Babur are launched towards Indian Carrier from a distance of 600KM (which have 1500KM range) none of your radars or patrolling jets will be able to "stop" this from happening and this is logically doable. Now let it be submarines or second best harriers, they have nothing to do in this equation as what they could prevent has been done.
For Pakistan to knock your AC down, we need one shot of low-yeild warhead. For India to survive an incoming attack, it would need to neutralize every incoming attack. What if mix of 30 babur and carrier killers are launched together? How many of them do you think you can bring down with air-defense missiles? To be able to survive, you need to be 100% successful in neutralizing every incoming missile but for us, all we need is a 3.3% success. big deal?
As I mentioned, bringing Indian "giant" down will be a medal Pakistan would like to get very early in the war. Mind that our navy is very small as compared to Indian marine power and neutralizing as many Indian marine asserts as possible using air and missile would be one of the priority.