I nursed my first within about 3 minutes -- as soon as he was sorta dried off and wrapped in a blanket. We have a photo of me laying on my back nursing him still in the blanket. I was hemorrhaging, and the midwife was hoping that nursing would be enough to stem the flow. It wasn't, but I was glad to have that connection with him. However, that did not make nursing easy for us; because I was transferred to the hospital for emergency surgery and he developed the shakes from low blood glucose (he was HUGE -- 11.5 lbs), he had a bottle of formula while they were repairing me. We had so much trouble nursing after that, and it took eight weeks to sort out breastfeeding.
I nursed my newest baby, who is now 6 weeks old, within probably 15 minutes, although it felt a lot longer than that. After getting out of the tub and getting on the bed so the midwife could check me out and I could deliver the placenta, I made DH hand me the baby so I could nurse him. He latched on by himself -- that instinct kicked right in -- and has been a perfect nurser ever since. We delayed weighing and measuring (I opted out of vitamin K and eye drops) until I was ready to switch breasts, which was about an hour later. He nursed for another hour then fell asleep and stayed asleep until much later that day; I just let him sleep (and slept myself) and then got started in nursing. He never lost any weight, which is quite unusual for a newborn.
However, they do go through a serious sleepy period, and it could be really, really hard to nurse for the first time during that time. If you can, nurse before that period as much as you can. If you can't, you still will be able to have a successful breastfeeding relationship.