Babies get into routines very easily, the trick is to make them the right ones.
The baby will only be able to sleep through the night when he does not need to feed at night.
After the recovery of the birth weight and the beginning of the stabilization of the growth, +/- after the first month, the baby will begin to increase the time of continuous sleep progressively. At this age, a bigger nap (about 4 or 5 hours) is already very good.
Normally, at 3 months a period of intense growth begins and babies tend to regress regarding to sleep time because they need more food during the night. After this phase, they quickly return to longer sleep. At this age, 6 or 7 hours in a row is great.
Later, at 6 months, we have a new peak of growth. After this, the true complete nights begins with between 8 and 12 hours in a row …
What to take into account: a baby only sleeps well if he/she is well fed and with nothing to bother. A tooth that is sprouting, a cold or even a colder night and we will have wake-ups during the night, the important thing is to calm the baby without letting him really wake up. Never start cuddling, talking, or any other activity that stimulates your baby. Keep the light as low as possible and only change the diaper when it is absolutely necessary.