Xibei San Ma
Cuba is small island nation low on IC and does not have much influence in the world. You can change that by expanding to the Americas and taking all of the Caribbean islands that hold something important.
At the beginning don't worry about IC. You will need up to 7 infantry divisions, 6 transports and some convoys, so quickly create them using the little IC you have. It would be smart to build some smaller boats to defend them but that is not required. When you're done you will be in a strange time period where all the wars will begin. You're going to have to conquer a lot to become a threat to Europe and the United States.
Since your nation is weak, you should only concentrate on infantry. Also, don't forget to work on new artillery. In the beginning you will only have 1 tech slot but in the future you will have more.
Work on influencing the Axis because your future is there and you will need about +120 to join during war time. You can change the world by joining them, even though you're tiny. In the end you will have many puppets and you'll become one of the major Axis leaders.
The Dominican Republic has 2 provinces and that will help. Declare war on them and land 6 infantry divisions in the north. Now hit the rest of the Dominican Republic. You'll have to annex the nation before the US cancels the non-aggression pact with you. If you don't have any transports, retreat your armies up to Cuba and build some. Now make 1 factory on your main island. Build some militia if you have some extra IC. It will gain experience with your infantry.
Once you can supply troops in the Dominican Republic you can declare war on Haiti. Move all your troops to the southern province and let them take the upper province which will spread the units and then attack Port-au-Prince an take it. Then annex. You now control 2 major provinces. You have to move quickly before the US cancels their non-aggression pact with you. Continue to spam infantry.
Central American nations are rich in terms of IC which can help. Hit El Salvador and annex it. Then take Guatemala. This only takes 10 units at this stage. Quickly rush to Costa Rica and liberate Central America as a nation and let them spam troops. Once they have around 4-5 divisions, move your troops around because your next move will change the world.
Once it is 1939 you should join the Axis and grab all of the Dutch, French and British colonies in the Americas and liberate them as puppets. Keep Jamaica though. This area isn't defended. Take military control of your allies and take over France and then London. This will end the war early but you can't rush into this. To take the main island, you'll need about 50 infantry divisions. Taking military control over Germany is also very helpful. Land in Dover and sweep around the islands. Don't liberate Scotland, England, or Wales, or the UK surrender event wont happen. Now you move all your units to Africa and conquer it. Then prepare to fight the Soviets.
The US won't declare war on you unless you declare war on them, which you can do with all the units from your puppets. You will probably need to buy a colony from Italy that is worth something, in case the US overrun you. You will use all your armies against the Soviets because you don't need to defend the French coast so you'll have extra armies to spare. You can also liberate all the British colonies and then you will be stocked with puppets.