Well "Assistant Conductor" is a loose term. You go to Conductor school, you wear a Condutor hat, you get Conductor memos, etc. The two big things you lack when you first come out of school are qualification and pay rate. In order to be a Conductor you must be qualified on the territory your train will be running over, if you are not you can only be an assistant Conductor for that route. To get qualified your crew base must decide to pay you to qualify, or you may do so unpaid, most people wait to get paid to qualify. To qualify you make a series of trips on the head end of the train and note physical characteristics including signals, curves, sidings, double track, wyes, yards, etc. so that you can identify your location almost down to the milepost if you ever have to in an emergency situation. Once you know the territory you take a logistics test that if passed will give you qualification. Once you get qualified you have every right to a Conductor job as the next guy if you have the seniority to hold the job. In some low seniority crew bases like Washington South you could be on a Conductors job within a few months.
As far as moving to Engineer goes, you can change crafts whenever your contract for your current craft allows you to change jobs. For example, some Conductors sign a contract when they first hire that requires them to stay in a certain crew base for a certain period so that the crew base gets their investment back that it took to train and qualify you.