Aircraft carriers are not particularly well suited to be supplied by cargo aircraft.
The largest cargo aircraft with the strengthened landing gear, arresting hook, and catapult attachment used to be the C-2 Greyhound. It had a range of approximately 1,500 miles with a 10,000 pound cargo. It was retired on July 28th, 2026. The C-2 has been replaced by the CMV-22B Osprey. It has a range of only 1,150 miles and a more limited cargo capacity of only 6,000 pounds. 6,000 pounds isn't nothing, but it's not a lot either.
There's not a lot of stuff within 1,150mi of the Arabian Sea. Your two options are one of the US bases in the southern Persian Gulf (Kuwait is too far) and Diego Garcia. Neither are ideal. In both cases you're doing a transfer out in the field.
On the other hand, the C-5 Galaxy can carry 120,000 pounds to a range of 4,800 miles. You can fill it with food in the continental US, fly to Hickam AFB in Hawaii, refuel, and fly the rest of the way to Guam. On the return leg, an unladen C-5 can fly directly to the 22nd Airlift Squadron's home base California without a layover.
The C-17B Globemaster is smaller than the C-5, although it's nearly as capable. With a 160,000 pound cargo, it has a range of 3,200 miles, (the C-17A has a shorter range) which is just short of the 3,800 miles to get from Hawaii to Guam. I don't know how much cargo it's capable of carrying 3,800 miles, but on the order of 100,000 pounds is a reasonable guess. It is also capable of an empty flight back to the US without a layover.
The relevant phrase is underway replenishment (aka UNREP) https://en.wikipedia.org/wiki/Underway_replenishment
It's been the basis for at-sea supply of long-endurance ships since ~1910 when refueling oil became a key blue sea naval requirement.
Modern example: https://m.youtube.com/shorts/kzncvGBj-88
Mostly tensioned cables carrying hoses (liquids especially fuel being the highest volume / limiting factor), some palletized transfer over cables, and some helicopter lift (because the flight pads/decks are already sitting next to each other while everyone is waiting for fuel to finish).
The Osprey is air refuelable though, isn't it? Each flight is roughly one pound per person on board.
It's also roughly 2800 nautical miles from Kuwait to Diego Garcia, so regardless of where the carrier group is, it should be at most a ~6 day round trip at 20 knots for a supply ship from the closest of the two.
That assumes there is no way to airdrop watertight pallets of food (e.g. steel drums loaded with cans and MREs) into the water, then retrieve it with RHIBs or helicopters.
Trying to do 4 Osprey flights per day, with refueling, for spartan resupply... is going to be tough. Sure, it's not impossible...
In such a situation I expect you'd have a lot of other stuff competing with food for that lift, too, like spare parts.
Not really relevant but a fun anecdote:
I can't speak to how much cargo was on board, but I did a Hawai'i to Guam leg on a C-17B that was carrying palletized cargo.
One of my better Space-A experiences. Crew was great, flight was smooth. I preferred it over the KC-135 leg, despite the more spartan conditions. The aircrew let us toss out sleeping bags and packs in the aisles between cargo and get some sleep.
I thought it was well-known that unmodified C-130s (Look ma, no hook!) can land and take off from US-sized carriers successfully. Ergo, in a pinch, everyone will be getting their chicken nuggets and canned corn.
When we had crews that had trained for it and recent operational experience with the capability, it was deemed not worth it.
Trying to stand it up in an emergency now is asking for trouble.
You'd have to be in a really dire situation to risk the carrier and aircraft this way.
No, in a pinch, you're just beclowning yourself with your utter ignorance of carrier air operations.
They're not striking the entire air wing below just so one C-130 can land and take off, and that's assuming a stunt pulled by one elite test pilot was replicable by a bog-standard junior C-130 pilot.