While the above method will work, I was able to achieve this in my first season of Be a Pro.
Start off with the team of your choice and make the roster. Set the skill level to rookie to make things a little easier on yourself.
You do not need to do every game, maybe every three but sim the game to the third period and then intervene. You should have at least B's across the board from coach feedback. Put in a couple of goals, maybe an assist. You should finish the game with at least a B rating overall.
By November 15th in my first season I had been promoted to the first line with 37 points and an A+ in offence, B in defence and B+ in team play.
I was playing as a winger for the Leafs, a rebuilding team may allow you to progress quicker. At the time of promotion I was only a 72 overall.