A delegate and logistics are required, but above all you need people wanting to participate and compete.
You need to find a way to see if there are more people interested in solving puzzles and are willing to build a community with this shared interest.
As you can understand it is very hard and pointless to make a competition just with one or two people.
My suggestion is to teach people that you know and see if they like it. Hopefully someone will and can further make cubing more popular in Cuba.
As for organizing a competition, cubing is an exercise in skills like dexterity, logic and mental ability.
It has absolutely nothing to do with politics, so I don't really see an insuperable problem organizing something in the future if enough people are interested.
Good luck.