At 2 months old, your baby is still a newborn, so they’ll still be sleeping the majority of the time. However, towards the end of month 2, you might start to see more distinct sleep patterns taking form, which could include longer stretches of sleep at night.
Until then, your 2 month old will be sleeping up to 18 hours a day, staying awake for no more than 2 hours in between sleep times, so your sleep schedule should be planned accordingly. However, keep in mind that at this age, it’s better to implement a sleep routine as opposed to a schedule. A 2 month old sleep schedule might be too ridged for the age, while a 2 month old sleep routine will allow more flexibility, but while still introduce good sleep habits. They’ll still need to be fed frequently, so don’t expect to be sleeping through the night quite yet.
You can learn more about 2 month old sleep and what it looks like here.