Hi Buddy,
I know the situation isn't pleasant especially if you call the lane before hand, but as some other chat responses have indicated, it is the most casual 'normal' game mode. If you decide to play blind pick, the risk of that situation happening is raised because nobody is 'locked' into any sort of role.
It's a laid back mode essentially, so the best advice I'll give is if you play blind pick, be open to playing any role. Again, it's laid back so though you should play your best, don't let it stress you out or frustrate you.
When I started playing back in Season 2, blind pick was my go-to. I usually let everyone claim their roles and took whatever was left. Usually that meant support lol but it was what it was. To me, if everyone got what they wanted, I thought it raised my team's chances of achieving victory. I didn't mind that much because it was just a normal game.
We are fortunate now to have draft modes that allow us to play the roles we want, especially since old draft didn't lock you into a role. It only allowed you to ban champs and not allow for the nerve racking duplicate matchups.
If you want to play a specific role, play the modes that allow you to do that :)
Good Luck on the Fields of Justice!