Other people might say differently - but I did the single-rider line five times during previews on Tuesday, and managed to get all positions.
The trick was how they were handling where the single-riders went. If one person was in standby, they grabbed a single-rider to make a pair, and the SR became a Pilot.
If a party of three was in standby, they grabbed a single-rider to make 4, and that SR became a Gunner. The one time I did standby myself solo, they actually grabbed a single-rider to fill the Engineer spot on the previous car before asking me how many were in my party. (Lucky for me, that put me in as a Pilot on the next car.)
Statistically speaking, you're probably most likely to be assigned as an Engineer, then Gunner, then Pilot.
But honestly, people openly traded spots - some people didn't want to Pilot. So, even if you get assigned as an Engineer, you might be able to trade.
(To be fair, things were weird on Tuesday - there were so few people in line at times that they once actually made a car entirely out of single-riders at one point - which was hands-down the most fun of my six rides.)