Well, if we're dealing with a clutter earth where the League and JSA co-exist, I'd say that Argus formed as a support team for the heroes Roosevelt recruited during WWII. As capable as Jay, Allan, etc. are, they'd still need guides, medics, tech support, cooks, guards, drivers, and all that. So I'd have Argus begin that way; as a hodgepodge group of military officers and technicians put together to assist the superhumans. And as the War continues and the JSA expands and starts dealing with more complex missions and high-tech and magical problems from the Axis, Argus grows with it.
By the time the war ends, Argus has become a fairly large organization unto itself, but still based around superhuman support. But once the JSA goes missing after McCarthy's BS, the government realize they've lost their first line of defense and have no counter for the growing number of superhuman and supernatural threats facing the nation. So Argus is expanded to fill that void and becomes a fully fledged new branch of the military.
In my head canon, Argus (it's not an acronym for anything because those get old fast) is, as a whole, roughly as powerful as the big hitters in the League. If you could pool all of their resources together in one place, they'd be about as effective as a Lantern or Superman or Flash. But it's thousands of soldiers, scientists, doctors, mages, etc., with first rate weapons and technology, rather than just one person with an insane amount of raw power.