At some point, all of the dragons will meet up. This doesn't have to be at the beginning. They can wander around for a few days, maybe meet one person or a whole group. Eventually, everyone will meet up somewhere.
The thing about plummeting downhill at fifty miles an hour on a snack platter - if you realize it's a bad idea when you're halfway down, it's too late. — Rick Riordan, The Son of Neptune