In 1936, they were still recovering from the War of the Triple Alliance which had led to the deaths of many of Paraguay's soldiers and civilians. The war had caused an economic depression, which was only worsened by the Chaco War with Bolivia (another poor country) which had ended only half a year earlier. Although Paraguay managed to win this war, the Chaco Boreal region still remained heavily disputed. Despite having a large pro-Nazi/German community and a Axis sympathizing dictator during World War 2, Paraguay would end up joining the Allies against Germany in the closing days of the War in Europe because of aid provided by the United States.
The below is one of many player suggested strategies for Paraguay. Bear in mind, due to the dynamic nature of the game, it may unfold differently for other players.
Even though Paraguay is a landlocked nation with almost no industry, manpower or resources, Paraguay has a neighbor called Bolivia that is in a very similar position. However because Paraguay is a communist country it can justify wars right from the beginning in 1936. What this strategy consists of is to justify a war as soon as you can against Bolivia. Once you have your war goal ready, you will stay in a defensive position on the border with Bolivia because the Bolivian AI will endlessly attack your line. After a period of time the Bolivians will have lost most of its manpower and equipment attacking your line and they won't be able to break through. When you see that the Bolivians are low on equipment then you can start to push and invade their lands without too many problems. Again though the key is to be entrenched and let their army grind away on your front line until their troops are weakened. Once this happens only then should you put your army on the offensive. It may be worthwhile to consider building land forts and infrastructure on the border before the war to make things easier on your army when the Bolivian AI starts to grind away on you. Then when you capitulate them, you will just annex them. After this you can attack other countries (the best option would probably be Chile). Be warned though no matter which other neighbour you attack next, it will be more difficult. Chile has among the strongest infantry division templates in South America at the very start of the game, and being only a few tiles wide you may have to deal a long war as you take the country one tile at a time as you make your down to the capital. In essence Chile will do the same thing to you as what you want to do with the Bolivians. Alternatively you could try to attack Peru or Argentina however both have larger armies and more manpower meaning in order to win you need finish the war as quickly as possible before they can produce more divisions. It is probably worth producing paratroopers for these options as you can land forces behind their lines to either pull forces off their front or conversely to pin down forces so they can't reinforce divisions your frontline army can defeat. It is strongly advisable to not attempt to attack Brazil unless you have conquered at least two other neighbouring nations to gain more manpower and factories. Another option is to join the Second World War by joining one of the factions, however if you do this while tensions are high and you are attempting to conquer one of your neighbours it will likely result in the other nation joining an opposing faction. The most obvious faction to join would be the Soviet Union in the Comintern as you already are communist and can join at any point. Or the Axis if you go fascist though this means one would have to switch ideologies. Even though you can join in on the side of the Allies, this would probably result in much less territorial expansion.