Bioshock Infinite‘s 1999 mode is tuned harder than most gamers can tolerate which is why it is saved until you complete the game once, however there is a way to unlock it right from the off.
Players who are looking to punish themselves from the get go can enter a cheat code to unlock the 1999 difficulty. The code is: Up, Up, Down, Down, Left, Right, Left, Right, B, A. On PlayStation 3 replace O and X with B and A, and on PC its Cancel and Confirm.
So if you fancy punishing yourself for no good reason then enter that code at the main menu and jump into 1999 mode.