Especially if mom is breastfeeding, consider co-sleeping, either in your bed or in a co-sleeper bed that goes next to it. Babies and moms will synchronize their sleeping cycles and not even wake up fully to nurse in the middle of the night.
Bottle fed babies usually sleep through the nights pretty young, since the formula is more filling than breastmilk. (It takes longer to digest, so baby doesn’t feel hungry as soon.)
Consider the Amby motion bed if you’re not into co-sleeping. It moves gently when the baby moves and soothes light sleepers back to sleep without waking up all the way. It’s like having the baby rock her own cradle!
Sleep train early. I did it at 6 weeks. Because I did it so very young, I modified the times you usually find in books. Here’s what I did:
1st night: put her down with lots of hugs and kisses. Say “Good night!” and leave, closing the door. Let her cry 1 minute.
Go back into the room, (don’t pick her up!), reach in and pat her tummy and croon a bit. Say “Good night!” again. Leave and close the door. Let her cry 2 minutes.
Back into the room, (don’t pick her up!), reach in and pat her tummy and croon a bit. Say “Good night!” again. Leave and close the door. Let her cry 3 minutes.
Back into the room, (don’t pick her up!), reach in and pat her tummy and croon a bit. Say “Good night!” again. Leave and close the door. Let her cry 3 minutes.
3 minutes is as long as I would leave a 6 week old crying alone. I’d only repeat 3 minutes once. If that doesn’t do it, give up for the night. (It did it for our girl and for most other babies I’ve done this with.)
2nd night: same thing. Only this time, with ours and with most babies, you only get to the two minute stage, and they fall asleep.
3rd night: same thing - except almost all of them fall asleep right away.
It’s amazing how effective this is. The first night is utter torture, and the second night painful. The third night is miraculous, and you’ll find yourself poking her awake to make sure she’s still breathing.
This can also be done with an older infant or toddler, but it’s harder. Increase the times to 5, 10 and 15 minutes respectively. If you’ve waited until you have a toddler who climbs out of bed, you have to sit next to the bed, not making any sounds or eye contact, and put the child back in bed every single time she gets out. It can be awful - I had one child I had to do this with literally 87 times in two hours. But again, three night of torture means the next 15 years of peace. Then they start staying out late and you’re not sleeping again!