Our Son was sleeping throught the night at 1 month old!
My Mom helped us the first two weeks and showed us a few tricks.
#1- keep on their schedule of food throughout the day. Don't make them wait more than 4 hours for milk.
#2- Create a night time rital- Ours was to turn lights low and turn off all noises.
#3-Don't play with your infant before bed..be boring. No lound noises or active songs during the night time feeding and changing.
#4- Swaddling our Son played a HUGE part in him sleeping through the night.
#5-Once your child is 1 month old they are drinking enough Formula or breast milk and will NOT need to eat at night.
#5- part2- If your child wakes during the night, He/She is NOT crying from hunger. Do NOT give a bottle, they will expect it and NEVER sleep all night.
#6- This was the hardest for me- My Mom had him with her for the night when he refused to sleep from Midnight-2 am. (We were pretty miserable) She KNEW he wasn't hungry, so she kept talking to him (without picking him up from his bassinet) saying he was find and to go to sleep. He cried a total of 20 minutes ( a LIFETIME for a parent) and then went to sleep. From that point on he was asleep all night.
This is what worked for me, but feel free to do what is best for you and your baby.