It's been so long ago that I don't remember but what I lost the first week, but I did lose 70 pounds in 3 months. Then again I started at 330 pounds so it's pretty normal to lose quickly at first when you're that much overweight.
The induction phase of Atkins lasts 2 weeks. The purpose being to rid your body quickly of the excess carbs...because once you do, the cravings go away. I follow the 1972 Atkins so my first two weeks were nothing more than protein and salads. I ate whenever I 'felt' hungry and know I was eating close to 3000 calories the first week. As I slid into the 2nd week, the cravings were less so I ate less and my calories probably dropped down to around 2000. After the 2nd week you can add carbs back in slowly, but I kept mine low deliberately. I never ate more than 30gm of carbs per day and it was always in vegies.