..it will vary!
There really isn't a set date as to when your baby should or will sleep through the night.. it's just too many variable and babies are SO different from the next.. variable likes..
- a bigger baby vs smaller baby (aka calories needed or not)
- a fussy baby vs content baby
- colic baby vs non colic
- where/how they sleep
Perhaps by month 4 I would say a baby should be snoozing through the night.. Monroe was tiny being born, so it took him longer to catch up and finally be full in his calorie intake before bed!