You can attack early and risk the wrath of the US. If you start in the South just make sure to put 2 solid divisions in every port and build coastal (& yes land forts) in all your ports. I say land forts because amphibious invasions drop troops on both sides of a port so then when they attack its the land fort thats important for defense. The problem is sooner or later someone will join the allies or once your all the way up to colombia the US will simply land in Panama and roll down. The major issue is this gets their war machine rolling early which is bad news for the Axis.
The US begins the game not guarenteeing 3 or 4 nations in the area. I dont remember exactly but Cuba and Ecuador are 2 of them (perhaps Dominican Republic & Haiti? are the others?). Join the Axis and join the war against the Allies and spend your time snatching up every island belonging to the British or French. Also grab the British/French/Dutch territory in northern Brazil. The French spot is a tough one as it will turn Vichy and be a possible landing point for the Allies. Anyway you want to grab and reinforce the isles to push the UK further away from being able to invade you. This will keep you busy until the US gets involved. If you want to be really ambitious. License LC's from Japan. Before the war is going to launch send an invasion force (maybe 4-5 INFx3/ART) to one of the Italian isles. Before Sept 1st ship them west out of the med. As the War starts, you join in, and then take Gibralter and reinforce it. What this does is not only help the Axis and hurt the Allies, but allows you to receive Lendlease from Italy. You can now get lendlease constantly from all 3 (Germany, Japan & Italy).
The biggest problem Argentina has is low manpower, and the more you use on ports the less you have for combat. What may be a good suggestion is setting up your trades so you make a ton of money. Delete all land forces and PL all units from Germany & Japan. Japan gets the Jungle modifier way before Germany (if Germany does at all) so you want to wait until you see they have it in the PL list and get your Infantry from them. This way you have better "quality" troops.
Actually Brazil is a better nation to play in this regards unless you have an affinity to Argentina. They have a better Industry, Economy And much much larger Manpower base. Hope this helps.