As far as I know, the Argentinians expected the British to act much in the same way as Portugal did during the Indian annexation of Goa; an initial overwhelming victory would pretty much force the previous imperial holder to just settle, both due to international pressure and simple facts of distance, combined with the relatively low value of the islands. On top of that, while the US and UK were close allies, the Monroe doctrine would have put some strain on the US-UK relationship, and thus severely limiting what would be expected of US support in this case.

Logically, the Royal Navy would have to be central in any potential recapture of the Islands. The Royal Navy (RN) was in the beginning of the 1980's still a relatively formidable force, both in tonnage, ships, submarine, supply capabilities and technology all far superior to the Argentine one (ARA), but was also facing severe cutbacks, and thus hugely limiting it's future power projection abilities. Especially over a now mostly waned, but still stretched empire. On frigates and destroyers alone, the RN outnumbered ARA by something along the lines of 48-6, never mind the Argentinian dependence on obsolete cruisers, or the modern RN submarine strength.

Even considered these strengths, in a head on fight, the RN would be facing severe problems against a fully occupied Falklands Islands. One of the problems would be air superiority, as with the remoteness of the islands, the UK would be almost completely limited to the aircraft they could bring on carriers. The Vulcan raid of the Stanley airfield from Ascension island would show how difficult it would be to get military airplanes in the area. Even HMS Hermes, the future flagship, and carrier of over half of the 28 harriers brought to the theater, of the RN task force to retake the islands, was scheduled to be decommissioned in 1981, and had a faulty screw. By comparison, the Argentinians were fielding 30 Dassault Mirage 5 planes and 50+ McDonnell Skyhawk fighters in their air force alone. The ASA also had access to additional, but inferior, fighters.

And on top of that comes the infamous Exocet anti-ship missiles, which would prove a significant deterrent for the RN throughout the war, and the fact that maritime landings, even under the expected troubles of establishing air superiority are a logistical nightmare seen from a military point of view.

All in all, I don't think that the Argentinians expected the UK to even fight back. And even if they did, they would not expect them to be able to launch a large scale war against Argentina in the South Atlantic. During after the landings, they also seemed to count on the fact that the RN taskforce would rapidly deteriorate in strength so far away from home ports, as they launched little-to-no offensive actions.

Even for the British, the fact of how haphazardly the RN task force was scrapped together, even shows how hard the British themselves had it: Its flagship and lead hangar was scheduled for decommission, half of the ships were merchant navy ships, a large part of the troop transports had to be handled by actual cruise ships, many sailors, soldiers and marines had not returned from Easter leave, and the ships leaving the UK mainland even had large amounts of practice ammunition aboard. They were even going into enemy waters against an enemy, which they knew had Exocet missiles, and even with their destroyer defense ring, they knew they would not be able to reliably counter. On top of that, if the Argentinians could force even one of the two RN hangar ships, the HMS Hermes and HMS Invincible, the operation would be over, as they were already at full strength going head to head with inferior fighter numbers (Although, unknown to the general military leadership during the war, Reagan would have been willing to loan a US hangar ship to the RN, in case they lost one).