Visa to Cuba
Under the current regulations, there are 12 permitted reasons to travel to Cuba. You will be traveling under the category - Support for the Cuban people.
You will be supporting Cuban people by coming to our wedding. Our rehearsal and wedding venues are privately owned businesses and not affiliated with the government. So, by attending the wedding, you already qualify for the category.
The general idea is that you can purchase the tourist visa (tourist card) through your airline or in advance. We highly encourage you contact your airline directly to find out what needs to be done ahead since the process changes all the time.
We have flown JetBlue (NYC) and American Airlines (Miami) to Cuba when we travelled. In both instances, we were able to purchase the tourist card at the gate before departure.
Fore more information
https://www.viahero.com/travel-to-cuba/how-to-get-a-cuban-tourist-card