Can you elaborate on your question a bit? I'm assuming by local you mean Cubans in Cuba, but it's unclear. Clearly some of Cuba's problems are a result of the decades long trade embargo the US has had in place. The United States has the largest market, industry, and financial influence in the region and it is one of Cuba's primary natural trade partners and former colonial master. Even for a large and more economically powerful country like Mexico or Canada, an American embargo would be catastrophic at least in the short term.
I don't think this is in dispute anywhere so it would seem on the surface you must be asking a more specific question...
Is there any point to this argument? Yes. The question is to what degree Cuba's problems are a result of American action vs. the Castro government's actions or pre-existing economic problems prior to the revolution.
I wanted to know if the US embargo had really created the poverty there or is it more their local governemnt, and if so how?
I'll respond directly to this, since your initial question was a bit broad. I'll also give you the short version. Let me know if you want more specific answers. This is going to be the TL;DR version, since there are a lot of complex, overlapping laws that combine into what we currently know as 'the embargo'.
First, US law prohibits trade with both Cuba AND the US. So if a French company wants to sell diapers, they have to have economic transactions with Cuba OR the US. Obviously there is more money in the US, so the French company will sell there. In order for Cubans to buy the French diapers they have to buy them from a third party wholesaler, who usually specializes in companies with iffy economic/legal situations, like Cuba. This jacks up the price of everything. That Coca-Cola you're drinking in Cuba? Imported from a third party who buys it from the plant in Mexico (true story).
Second, Cuban government property that finds itself in US hands can and will be seized in compensation for US property seized during the Revolution.
Third, combine points one and two: If a financial institution is doing business with both Cuba and the US (what major bank wouldn't trade with the US?) then they are in violation of US law. This means that if they want to continue to do business with the US they must pay a huge fine, upwards of tens of millions of dollars, if the US finds out. The US will also demand the freezing and later seizure of Cuban funds held by the bank. This has happened a LOT. In response Cuba uses super shady practices to launder the American dollars it receives through tourism back into the international market. The people who do this for Cuba, whose identities aren't public knowledge in Cuba, at least they weren't the last time I was there (2 years ago), charge a cut of every dollar laundered, meaning that Cuba gets 85-90 cents of every dollar spent there due to having to use an international back door.
Fourth, you want to invest in Cuba? Then you can never invest in the US! A company that wants to build a joint hotel chain? That company can never build anything in the US. A government/institution wants to loan Cuba money? No trade for you! Brazil loaned Cuba money anyway under Obama, but because it is a government and the timing they have gotten off scott free.
Fifth, if you are a ship that docks in any Cuban port you cannot dock at a US port for X months (3? 6? I forget the exact number).
Cuba was never extremely wealthy, but it did fairly well for itself before the Revolution. These restrictions make it extremely difficult to function economically since everything must be done through third party intermediaries who demand their percentage points and everything seemingly simple demands extra steps to avoid a US ordered penalty against a company/financial institution.
Hope this was a good summary.
Edit: Only going to add here that the USSR created a parallel world economy among socialist countries that didn't give a damn about US law to begin with, so the affects of the embargo were diminished, though still really annoying, from 1962-1991. From the fall of the USSR on, however, the affects have been pretty devastating.