I did this in HOI3. My approach was to build an army exclusively of 3xMOU+1xENG and 3xMAR+1xENG, this really cuts down on tech required and most of the continent is jungle or mountain. No proper airforce but I did create a 1938 and two 1940 CTF's. Started with 3 IC runs which gave me around 120 usable IC which gave me 3 years to create my forces which was 40 division plus navy. I went to war in 1941 after the Americans were at war with the Japanese. From there it took me a little over a year to conquer south America up to the Mexican border and all of the west Indies. Over the next few years I sank much of the US navy in their rubbish attempts to retake Puerto Rico. I was a very fun game.
In HOI4 a few things will be different, the biggest being that you will be free to declare war without the US intefering (their guarantee no longer applies when it's 2 S.American countries fighting). Based on today's dev diary I get the feeling should be OK, provided too much of the continent doesn't get marked as wasteland. We know that government form is reasonably flexible and in HOI3 they started as paternal autocrat so you mightn't even have to change ideology if they start as fascist.