A big thing here is why the baby is waking up at night. Young babies are usually hungry - for instance, the formula my daughter is on has less protein which means it is less filling, so she woke up more often. Even though a baby can start sleeping through the night at a young age, that is most likely going to change in a few months when teething begins. My six month old daughter's schedule has changed numerous times over the last few months - she did very well earlier on, but began teething in her third month and hasn't stopped since, so her sleep schedule is all depending on how she is feeling. She just got another tooth this week so that explains the last three weeks of constant wake ups.
Lots of babies still aren't sleeping through the night in the first year - I've now opted for a more expensive concealer for the circles under my eyes.