Based on the discussion here, it looks like the trophy is poorly worded. It seems that the unlock is actually from maxing out your first weapon type, which is at 999999/999999. You can actually choose any weapon type for this; it doesn't have to be the one you started with. By "first", it means the first one you max, not the first one you pick up.
You need to max the proficiency of a weapon type, not a single weapon. Go to status and on additional stats you will see your proficiency with every weapon type. Get one of them to 999999 to unlock the trophy.
This is also supported in PowerPyx's trophy guide:
The maximum profiency score is “999,999”. Your procifiency increases every time you hurt an enemy. Even if your weapon’s proficiency is at maximum (e.g. 900/900) it will keep counting additional proficiency points in the background. So you do not have to switch weapons after one is maxed out. If you stick to a single weapon type you should unlock this at about 50% campaign completion. Just stick to one weapon type and it’ll come automatically on your playthrough.