As someone who didn't play BF2042 until the BF6 beta closed and I heard about the season pass, I discovered a couple of things that could help tremendously:
1. The weekly missions are tremendous for gaining progression in the pass. Don't skip them. They unlock week over week and should be your main focus, I've found it's pretty easy to knock out 3-4 per game.
2. Progression in general seems to be tied to XP gain. Weekends seem to have a XP multiplier as do the weekly showcases, so running Iwo Jima right now is a really good idea, especially during weekends.
3. Run and gun is far and away the absolute **bleep**tiest way to gain XP. I'm already through a third of the battle pass, because I spend all my time as engineer/support. If I'm not rezzing people, I'm driving, if I'm not driving I'm sitting backseat/repairing, if I'm not in a vehicle, I'm taking out vehicles, and if I'm not taking out vehicles, I'm capping objectives. Killing infantry is basically always just a means to doing something else, and when you play to the team's needs your XP will naturally soar.