It is not an accurate quote.
Fidel Castro 19 May 1977 said:
Some time ago, the United States was an English colony. If an Englishman were asked if the United States would be independent, he would have said no, that it would always be an English colony. Afterward, the colonies liberated themselves, a nation was established, but it contained slavery. The slave owners would have said that slavery would never disappear, but slavery ended, salaried workers came, capitalism came, it developed extraordinarily, large multinational enterprises developed, and if a reasonable man is asked now if that will be eternal, he will have to say no. Someday the capitalist system will disappear in the United States, because no social class system has been eternal. One day, class societies will disappear. But you can be calm, I do not foresee in a short time any change toward socialism in the United States.
So Castro predicted the United States eventually becoming socialist, rather than being destroyed.
Also, in the same interview he said:
I don't know when I'm going to die, I don't know if I'm going to die tomorrow, tonight, in an accident, from natural causes. I cannot know.
So clearly he did not hold the view mentioned in the OP.
The quote in the OP is somewhat similar to a famous quote by Bolivar
I swear that I will not die until I have driven the last Spaniard out of America
which illustrates the geographically inclusive nature of the term "America" and an additional reason that Castro would not say that "America" would be destroyed.