One reason you often do not get your role on that first game is often because the game originally had 3 or 4 people(out of 5) and when that happens, people take classes that they usually do NOT as Bots can be more horrible at certain positions than non bots.
So a good example of this is if I am in a party of 3 and we find a monster and no 4th hunter, someone will abandon their normal pick to make sure there is a human trapper since the bot trapper makes it easy for the monster to get away.
You can say much the same for medic as a bot medic does not always prioritize correctly. Often times, this is the bot I hate most and will always play if we have no medic.
Actually, you can make arguments for all the hunters.
If you could have some patience, enjoy what remains of the game, you very well may get your class next. This, I would think even if you hate the class, its more fun than loading screens and waiting timeouts. Besides, That next game could start well within the time it takes you to even get to your next match.
So, please quit leaving matches that do not start perfectly, they can grow into much more than you expect.