Gunslinger is a subclass of Fighter, but Fighters do not have proficiency with guns.  When they pick up the subclass at third level THEN they become proficient with firearms.

Question is, as a DM how do you handle a level 1 character that wants to be a Gunslinger?  Do you just make them deal with swinging a sword or shooting a crossbow till 3rd level?  Do you just go ahead and give them proficiency so they use they weapon they want to use?  What do you do?

Maybe they spend levels 1 and 2 practising during their down time and between fights. They're doing target practise, refining their quick draw, that kind of thing.

Quote from Stormknight >>

It's important to notice that a character doesn't need to be proficient with a weapon to use it - it's just not very optimal.

 I was going to say something like this. You can use a weapon without proficiency. And there are rules for practicing to gain proficiency.

If I were running a game in which firearms are common enough that the PC isn’t the only gunslinger in the world, I’d probably just add them to the appropriate simple/martial lists. If the PC IS the only gunslinger, I’d have them spend those first two levels, you know, inventing firearms.

All good stuff to think about.  Thanks everyone.

I have already established with the players that guns were invented in one kingdom but are still fairly uncommon there,  only becoming more rare the further away they get from there. The exception being the Dwarves, that once they got a hold of the technology, a number of craftsman took a really big interest in their design and improving upon it.

The player was talking about being from one of the more "Renaissance" type kingdoms so depending on their backstory, I may go ahead and give them proficiency or wait till level 2.  

Thanks again :)

I would explain it like, maybe a character belonged to a guild and they chose the path of the gunslinger when the guild had shown them the choices