There's no way around this rule except to have someone 21 (or on some lines, 25), or older book with you. As blueliner said, you have to have a passport or a government issued ID (with picture and birthdate) and an official (not hospital issued) birth certificate.
If you say you're married they'll have to see your government issued marriage certificate.
Again, any ship that sails out of the U.S. will have a drinking and gambling age of 21, and they DO
check. Your age will be imbeded in your onboard ship card.
My advice would be to find someone older to join you, or wait until you're 21