Ken Levine has been very open on twitter in the past, discussing development of BioShock Infinite with fans. He’s said a few times that you shouldn’t expect the first bit of downloadable content any time soon, but has now given a reason for this.
DLC Update: We are working on it – have been since the game shipped. Things are going well, but plz understand: game development takes time.
It seems they didn’t start work on the DLC until after work on Infinite had fully finished. We wouldn’t want them to rush anyway, as it could perhaps compromise the quality of the content.
If you really feel like you need to buy something for BioShock Infinite, then you can buy the Columbia’s Finest pack today, which includes weapons and perks previously only available with special editions of the game.
There’s still no word on what the new DLC packs could include, though there were previously rumours of a new companion character, and therefore a new protagonist? That would make sense anyway.