Have the junta harden its position after the defeat of the Falklands War, rather than allow democratization under Bignone, a hardliner stays in power like Alfredo Saint-Jean, with massive repression and international isolation Argentina would draw closer to the Soviet Union out of necessity of the regime for survival.
(IRL the Soviets became the largest trade partner of Argentina briefly after the Falklands War and even offered timid support during it, even as the military regime was still calling itself "anti-communist" and murdering left-wing people... the Carter grain embargo on the Soviets had already drawn Argentina closer to the USSR in the late 1970s)
You would also need to avoid the rise of Gorbachev, so the Cold War continues in full force until at least the early 1990s, giving time for Argentina to develop its nuclear program and medium range Condor ballistic missile even in the face of likely US and European economic sanctions in this scenario.
It is important to remember Brazil would also develop nukes in such a scenario. (And vice-versa)
A nightmarish scenario, to be sure.
A more benign version would be to butterfly away the 1930 coup, allowing Argentina to join the Allies in WW2 and follow a normal democratic path, Argentina becomes a major NATO ally, signs a defence treaty with the USA and gets placed under the US nuclear umbrella in exchange for allowing US telemetry tracking bases in Patagonia, much like Australia in OTL. However in this case it wouldn't be an indigenous deterrent but one owned by America.