Weirdly enough, it seems that sometime in mid-19th century,
Argentina stopped really caring about getting Falklands back and all there was to the dispute were some diplomatic shenanigans (well, with
one exception). UK was open to negotiating a transfer of sovereignty to Argentina, maybe even over islanders' heads and had the junta not been desperate for something populist that would make people not hate them, they might have succeeded in getting the islands peacefully.
Well up to a point, perhaps. School textbooks continued to talk of "las Malvinas" being Argentine, there were postage stamps produced regularly showing them as part of Argentina, etc etc.
The ruling junta opportunistically decided on an invasion in 1982 partly because their grip on power was showing serious signs of loosening, and partly because they misread some of the signals (both on the UK's willingness to defend the islands and how the international community - the US in particular -would react) But its not really true to say they manufactured the underlying sentiment from nowhere.