Likely paraphrased from this speech in 1959:

And this confidence we have in the Cuban people, which we have always had, is that we had when we reached the coasts of Cuba with 82 men, which we had when those men were reduced to a handful of 10 or 12, which we had in the most difficult moments, such as that defeat which was for us the first revolutionary battle, the faith we had when we were in prison and in exile, the faith which allowed us to be confident that if indeed we said as we did on that occasion that with a continuation of the campaigns against the revolutionary courts, we could rally a million Cubans in front of the presidential palace, we would be proven correct, that faith which led us to say that if we continued the campaigns against the agrarian reform, saying that the peasants did not want it, we could rally a half a million peasants with their machetes in the capital of the republic.

Given that this quote is often mentioned as coming from a speech in 1959 and the similarities in the wording.

The only other close match I could get from Castro speeches from this year is from this one, which is less of a match:

No one can allege that I am speaking as a demagogue. No one can charge that I am seeking to assuage the people. I have given ample proof of my faith in the people because when I landed with 82 men on the beaches of Cuba and people said we were mad, and asked us why we thought we could win the war, we replied, “Because we have the people behind us!” And when we were defeated for the first time, and only a handful of men were left and yet we persisted in the struggle, we knew that this would be the outcome because we had faith in the people. When they dispersed us five times in forty-five days and we met up together again and renewed the struggle, it was because we had faith in the people. Today is the most palpable demonstration of the fact that our faith was justified. I have the greatest satisfaction in the knowledge that I believed so deeply in the people of Cuba and in having inspired my companions with this same faith. This faith is more than faith. It is complete security. This same faith that we have in you is the faith we wish you to have in us always.

Some speculation:

This could have come from an early translation or a newspaper report in English where the translation was rushed or poorly-done but due to it appearing in a major newspaper it could have entered “canon” and since that point has become part of the circular-referencing that occurs in the media, unless it comes from a speech that I do not have access to.

This quote could also have been a conscious distortion of what Fidel said by being overly liberal with how his words were paraphrased - note how the quote in the image plays to this idea of some authoritarian dictator who seized power for himself in a coup whereas in his actual speeches he talks about having the support of the masses.

starting off my project management seminar with this castro quote and accusing everybody of latinx-based racism if they object

try translating it into Spanish in a few different ways and searching for that

I think it might come from his book In His Own Words. No idea on the page, though.

https://www.reuters.com/article/world/us/fidel-castro-en-sus-propias-palabras-idUSKBN13L05S/