World Cup, easily. A win like that would be legendary for centuries and break through unimaginable barriers. As famous as the 1980 Olympic hockey triumph is, it was hardly unprecedented. The USA won the gold medal just 20 years earlier in Squaw Valley.
To this point, as far as I know, the most famous USA soccer victory is 1-0 over England in the 1950 World Cup. Fantastic, but it didn't really lead to anything. It's like the Canes football history before their glory era began in the '80s. Prior to that, the landmark win in program history was upsetting Purdue one week after Purdue upset Notre Dame. Big deal. But in that era it was worthy of city wide celebrations and immense pride.
I've attended several Olympics. It's shared passion and joy with people from different cultures who you know you will never meet again, and have very little in common with, other than rooting for athletes wearing the same uniform over a brief two week window every 2 to 4 years. Pro football is not nearly as satisfying as college football from my perspective because it's so comparatively random and scattered from a personnel standpoint. The Canes are dominated by Florida players, primarily South Florida. Same for every region. Sure you recruit outside your base but the foundation is overwhelmingly local. Pro teams are tossed together by a contrived process called the draft. Even if a kid hated your team all his life, suddenly you own his rights so he's stuck. On the national teams the players have shared that dream all their lives, with few exceptions. Even in golf's Ryder Cup you occasionally have a goof who downplays it and calls it an exhibition, before actually participating. Witness recent examples like David Duval and Rory McIlroy. But once they get a taste of it they realize that representing your country brings intensity and passion that you didn't know you owned.
A legitimate run at the World Cup by the USA would summon all of that in exponentially higher doses than we've ever seen before, largely because we've never done squat in soccer and don't expect to. The America's Cup actually became a massive story when suddenly we were threatened. Grabbing something for the first time is markedly more satisfying that retaking something you've always taken for granted. The only people who want to pretend it wouldn't be a huge story are the ones who still want to believe that soccer isn't finally making big strides, that the premier league telecasts and updates aren't really happening. The hype was always overdone until less than a decade ago. Now it's legit. My brother in law has a relative who owns a chain of soccer apparel stores. Business is exploding. Major shopping malls throughout the country are approaching his firm and trying to get on the list for the next wave of expansion. The marketing is brilliant. I've been in one of the stores in Orlando. It's vibrant and always jammed with teenagers who know every foreign player while begging their parents to buy jerseys for them.
Sure, I've seen the Dolphins win and lose Super Bowls. The early '70s teams will always be the true Dolphins to me. The current group is merely a regulated version wearing a motion sickness logo and forced to perform in an incompetent venue. But even without being old enough to remember Csonka and company I'm confident I would still prioritize the big picture, and a World Cup success that grips 50 states, one of those moments when people remember where they were. Dolphin fans are a small insignificant piece of the pie. Other than pizza and most of my best wagering systems I prefer to share.