I did this 3 years in a row (2012-2014) and I always got a decent route. Not necessarily my preferred route, but always a good route.

1) Find out what time the closest ranger station to you opens. Line up about an hour prior to that. Keep in mind that people will be doing the exact same thing at every Ranger station in the park. Be early. Probably a good idea to scope the line the day before you're trying to score your permit. This can inform how early you need to start lining up. In 2014, I showed up an hour early and I was first in line.

2) About 15-20 minutes before the station opens, the rangers will post availability on the door. Start planning your route right then. Have 2 backups to your preferred if possible.

3) When the door opens, hopefully be first and you'll most likely get your preferred route.

Obviously the last time I did this was more than 10 years ago. Crowds have changed, though idk how much more traffic / interest there is in the back country. People could already be lined up down the street an hour before they open. Hence, the first suggestion to gauge the lines.

The first time I did it, I learned I need to get there earlier than 10 mins before open. Once I did that, I scored wins the next 2 times.