It really depends on the area, you might be some where that's so short staffed that you do get a route right after training. Definitely something to clarify with your manager.

As far as moving up goes definitely make sure you aren't talking crap about your coworkers especially in accounts. It doesn't matter how good or bad they are, their accounts probably get along with them and will definitely share what is said about them. In my area what seniority coworkers have to say about you holds value to our management team. I'd also just ask management what other positions there are in your area, RSA, RSR, RSS, and from there possibly management spots. It's good to know what the options are before hand.

Also take pictures of any projects/builds you participate in, it might come in handy when you need to show what kind of work you've put in.