My 3-day-old newborn constantly needs to be fed. It is affecting my girlfriend's sleep. We started pumping and bottle feeding but the baby still demands a lot. I've heard that this is common at the two week mark because of a growth phase. Since he was 1.5 weeks overdue, could he already be in that phase?
Babies eat. Babies eat a lot. Newborn babies eat a lot more than older babies. These are just the simple truths of raising children. Right now, your child has a very small stomach. They can't store as much food as we can and thus need to eat more often. Also, breast milk digests quickly, thus contributing to the need for more food, more often. This has little to do with a current growth phase.
Your baby will be in a consistent growth phase for the next 17 years 11 months and 27 days and even on after that. Our most recent baby is about a month and a half old already and he still requires (almost) continuous feeding. I know it is tiring but it is just part of having children. If your girlfriend is tired, find some way to help out; perhaps take over feeding with the bottle and let her catch some shut eye.
This part doesn't last long. Give it a couple of more months and you will find you have a different reason for not getting any sleep.