It would be quite helpful to know the specific source, as well as the scope of the essay you are working on? Your professors likely have a far better idea of the assignment than anyone on here, so I would defer to their judgement. You of course have 'liberty' in your assignment, no one can stop you from sourcing and writing what you wish, but that doesn't mean all sources are appropriate.

Personally I would agree that it is not the best of use of limited space to unpack a primary source dating to well before Castro's birth. If your question is focused on Castro's ascendancy, you would be wise to focus most of your research and word count on that, and summarise early on in the essay that US involvement in Cuba long preceded Castro's birth.

I apologise if this answer is too brief, but this does not seem to be a normal r/askhistorians question.

It depends on how it's being used. At first glance, from your description, it should be just as valid a primary source as any: you're starting out with the Spanish American War, after all.

However, I don't know what an 'extensive essay' means. Is this a 15,000 word thesis? If so, then yeah, you could easily fit such a citation in there. Is it a 5000 word essay? Then probably not - it's not the main topic, rather background context for the subject, so delving into the primary source material in that case is just superfluous. You can get infinitely better formed context from secondary sources, primary sources become more relevant the closer you get to the main topic. Explaining the context then throwing in a snappy quote from the US government like 'As a State Department report said...' to emphasise your point re: their justifications is about the extent that I'd go for in that situation.

It could also be a problem with how the source is being used. It's one thing to cite a State Department report regarding the Spanish American war to explain the US justifications/motivations, it's another to take it at its word.

Re: the last paragraph, as a general and reductive rule, primary sources should rarely if ever be cited that often unless doing original research, and for the topic at hand you weren't as these are questions that have been covered in a lot of depth already. A lot of undergraduate programs I know of recommend a 1:5 primary:secondary ratio to the students. This is to instill in them the fact that primary doesn't mean 'better', as an undergraduate all of the research you're doing has been done before by historians who have compiled it far better than you ever could, so you're more trying to show your grasp of the topic and its historiography than create something new and unique. You'll also be getting most of your primary sources from the footnotes of secondary sources anyway! However it's still useful to throw in illustrative quotes, statistics and stuff like that to at least get some practice working with primary sources. Basically, original research begins with a firm grasp of the secondary literature: only through studying it in-depth can you even identify gaps to be filled with original research in the first place.

I think you should really ask the professors though, in a nice and non-argumentative way, they can probably explain more precisely why they thought this.

In general, probably not.

First, let me applaud you for the effort - as well as the realization of it being irrelevant in your current circumstances if you're going to get flunked on the assignment.

That said, in general you should treat departmental reports to Congress or the Executive as secondary sources - and often not particularly good ones at that. Why? They come with all sorts of peril as they're usually written for political reasons and the analysis in them can be wildly skewed as a result. They can be useful to understand what leaders are being presented with, but they offer little in terms of why the leaders are getting them. That's part of your job as a historical writer to perform this analysis, and parroting a governmental report's conclusions as a definitive analysis on what the government was trying to accomplish in that time period is problematic.

Now, if you want to search through primary sources for US diplomatic history, there is a terrific set of documents available for them. Coincidentally, last week I went through Dallek's Franklin D. Roosevelt and American Foreign Policy, 1932–1945 for the first time in a while, and while it's a bit dated now it's still probably the best overall survey of the time period, especially of FDR's early years.

So for your topic, let's take a look at one section of what he writes about the US and Cuba in 1933:

(Following the coup against Cespedes in 1933), though [FDR] and [Secretary of State Cordell] Hull agreed to send warships, they did not want to send troops unless there were physical danger to members of the Embassy. “If we have to go in there again,” Hull explained on September 6, “we will never be able to come out and we will have on our hands the trouble of thirty years ago.” On the same day, the President urged the press “to lay off on this intervention stuff … That is absolutely the last thing we have in mind. We don’t want to do it..."

"[H]e also took pains to persuade the press that the twenty to thirty ships sent to Cuba were, with two exceptions, “little bits of things” which had to cover a seven hundred mile coast line and represented a very limited display of force. He remained convinced that direct military involvement in Cuba would distract from pressing domestic concerns and all but destroy the Good Neighbor idea."

Now what does he cite to come up with what's a pretty cogent analysis? Hull's autobiography, Time Magazine, several academic pieces, and Foreign Relations.

What's this last one? Well, from the Lincoln Administration all the way up to Clinton, the State Department has documented almost every cable and letter sent between Foggy Bottom and various embassies, and the best part? It's available online! So, what Dallek did was to go back and look at what Sumner Welles was writing Cordell Hull about the Cuban government at the time, although part of the historical analysis you'd need to perform is understanding Welles' particular importance to FDR and the influence that had on his decision making.

So that's what I'd suggest for a more robust primary source as you attempt to delve into US diplomatic history.

I wouldn't look at, rely on, or cite a single document from the State Department as the gospel truth on relations between the United States and another country. Bilateral relations are just so complicated that you simply cannot capture the nature of the relationship between two countries in a single memo.

When I wrote my answer to In 1962 former Republican nominee Alf Landon urged the US to join the European Economic Community, was this ever seriously an option?, I relied heavily on a number of different documents from the State Department's archives, including diplomatic cables and meeting summaries to provide context to US-EEC relations in the late 50s and early 60s. While I pulled some direct quotes from a few documents, I read through almost every document to make sure my understanding of US-EEC relations was complete. I also made sure to review contemporary primary source documents from EEC sources and try to validate the conclusions I drew against secondary sources, as well.

All that said, the State Department's archives are a really great primary source repository. There's a lot of good information there, from summaries of high level meetings between US Presidents and their foreign counterparts to very detailed memos and cables that give insight into the often highly technical matters that are the bread and butter of bilateral relations. Looking at or citing a single document is never enough; you have to be able take bunch of very granular data points and build them into a larger aggregate.