As soon as you meet the other prerequisites, you can take the feat. If you're a human staff magus, for example, you could pick up Weapon Focus (quarterstaff) and Weapon Specialization (quarterstaff) at level 1.
Edit: I'm a liar. Weapon Focus requires base attack bonus +1. You'd have to wait until you fulfill that requirement, then take/retrain Weapon Focus, then take/retrain Weapon Specialization. There might be a way to do this before level 3 (2 if you multiclass) if some race or other gives Weapon Focus, but I don't know it.
Bottom line, you don't have to be level 4, as there's no requirement enforcing that other than the "fighter level 4" requirement, which you bypass.
There might be a way to do this before level 3 (2 if you multiclass) if some race or other gives Weapon Focus, but I don't know it.
A human can sacrifice their bonus feat for Adoptive Parentage:
Humans are sometimes orphaned and adopted by other races. Choose one humanoid race without the human subtype. You start play with that race’s languages and gain that race’s weapon familiarity racial trait (if any). If the race does not have weapon familiarity, you gain either Skill Focus or Weapon Focus as a bonus feat that is appropriate for that race instead. This racial trait replaces the bonus feat trait.
No idea which race would qualify, but the GM probably might let it pass.
Weapon Specialization doesn't require BAB 1 by RAW, because it's usually included in 'fighter level 4th'. Nah, speak with your GM. I guess it's not the only way though.
Quarterstaff Master waives the Fighter 4 requirement so as long as you have Weapon Focus (Quarterstaff) you are able to take Weapon Specialization for it anytime.
You never 'need' to take it, but you probably will want to. The standard approach would be to take Weapon Focus (quarterstaff) at 3rd level and then Weapon Specialization (quarterstaff) as one of your two 5th level feats. Dipping other classes can let you take it earlier, but dips aren't usually a good choice for a Magus
Since the Quarterstaff is a Monk Weapon, it's also worth considering the Monk Weapon Skill Trait. It will give you a +1 Trait Bonus to damage early on, and later it will stack with Weapon Specialization.
If my group didn't really need me to cover arcane magic and traps(and didn't already have three front liners) for Curse of the Crimson Throne I think I'd give this a shot.
A new option is to use a Lantern Staff for the extra +1 fire damage. It also has a x3 critical multiplier instead of x2.
Since "[a]ny effects that apply to a quarterstaff, except those that require it be used as a double weapon, also apply to a lantern staff," Quarterstaff Master applies and you will be able to use a Lantern Staff with Spell Combat. Similarly you would get the benefits of Weapon Focus (quarterstaff) and Weapon Specialization (quarterstaff). The Monk Weapon Skill Trait (quarterstaff) would still apply even though the Lantern Staff isn't, itself, a Monk Weapon.
Since it is a metal weapon, you can have one made from special materials like cold iron, mithral, or adamantine to overcome metal-based DRs. That's especially nice at low to medium levels where being limited to wood can be a problem.
If my group didn't really need me to cover arcane magic and traps(and didn't already have three front liners) for Curse of the Crimson Throne I think I'd give this a shot.
Staff Magi are fun. Mine's a Hexcrafter/Staff Magus.