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In my experience, and I haven't been since 2019, the airline won't let you on the plane without the proper visa. and that's available at most or all airports.
I believe tourist cards are still needed. This website has all the info. We did their “This Cuban Life” tour a few years ago and HIGHLY recommend it!! We learned so much about the Cuban people and their daily life that we would have never learned on our own. We also got to see quite a bit of Cuba. While we usually travel independently, we were glad to have someone else do all the planning since some logistics are challenging in Cuba (like how to travel from one city to another).