Here is my spin, since I fly United all the time.
If you are not an elite, you are in Economy, not Economy Plus section. That section is reserved for elites, and only they can book it at time of booking. If it is full, elites will also be in Economy section.
A few days before the flight, upgrades start to clear for the elites. OP, this is VERY important. Are you on TED or United? TED has only E/E+ and nowhere for elites to upgrade. If you are on United, some of the Economy Plus seats may open up, as elites upgrade.
But you still won't be able to move to an E+ seat in advance. If there are a number of seats not assigned, usually United will only start to assign E+ seats to non-elites at the gate. So even on check in you may not get a different seat assignment.
Get to the gate early, approach the agent a few minutes after they arrive, and politely request a seat change. They may take your boarding pass to make the change. Then take a seat and DON'T bother them. I am amazed at how often ppl expect a gate agent to work the flight if they constantly have people asking them every 2 minutes 'did you get my seat?!'
If the flight is NOT full, then United really holds firm on not 'upgrading' non-elite members to Economy Plus. If there is an aisle seat there, and you want it, they may tell you that you can have it for a fee. Don't expect to move to an E+ seat after boarding, either. The FA's are very strict and I often see them discussing a 'game plan' to hold back the masses

if the flight is not empty.
Economy + is a huge revenue generator for United, so they do protect it, and it is one reason why they have such a loyal base of business travellers.
Hope that helps.