This is the current freshman orientation schedule: http://orientation.ucdavis.edu/first-year/schedule-student.html. I’m assuming that the 6pm end time is the latest it could go.
The way they did it a few years ago, everyone assigned to a given orientation leader was randomly assigned a registration time in 5 minute increments starting at the overall registration time. For example, the registration time for my orientation was 11am (I think). I was randomly assigned to register on the hour, the next person in my group was at 11:05, the next person at 11:10, etc. Assuming they do it the same way, I’m guessing they start registration at around 5pm, possibly somewhere around 4:30 depending on how many people are in each group, and do the 5 minute increments that way. Because of that, when you finish would depend on how lucky you get with your registration time. On the assumption that they do still do it that way, I don’t think there’s a way to ask for an earlier time so you can make your train.