Newborn babies sleep a lot. Expect your baby to be asleep for up to 18 hours over the course of 24 hours in his first few weeks. But he won't sleep for more than three hours or four hours at a time, day or night (Davis et al 2004) .xpect your baby to be asleep for up to 18 hours over the course of 24 hours in his first few weeks. But he won't sleep for more than three hours or four hours at a time, day or night (Davis et al 2004) .