When will babies sleep through the night first?

Three to four months. Babies are capable of one period of deep sleep (3-4hrs) per 24 hours starting at birth and generally drift in and out of lighter sleep states for the rest of their day. By 3mo their brain waves include mature sleep patterns and longer sleep is expected. Babies can learn to self settle soon after birth and return to sleep after they wake, though a brief feeding may be needed.Good routeins help.
Can happen within... first month!! It's all about the "Jassey Way", follow the advice from "The Newborn Sleep Book" and it will show you the way.