Yes, I'm biased in favor of leaving parents alone with their newborn for at least an hour (and two is even better!) Research and mainstream medical opinion backs me up on this. The first hour after birth is the golden hour that should not be interrupted unless completely necessary. Cochrane Review looked at all the studies available and concluded: "babies exposed to skin-to-skin contact interacted more with their mothers and cried less than babies receiving usual hospital care. Mothers were more likely to breastfeed in the first one to four months, and tended to breastfeed longer, if they had early skin-to-skin contact with their babies." An even more extensive article on immediate skin-to-skin contact between mother and baby explains that: "There is good evidence that normal, term newborns who are placed skin to skin with their mothers immediately after birth make the transition from fetal to newborn life with greater respiratory, temperature, and glucose stability and significantly less crying indicating decreased stress." Wow! Who wouldn't want to take advantage of that?!
Let me give you some pointers on how to make it happen for you, because this takes more intentional planning than you may think. Obviously, if baby is not doing well there will need to be more observation by the medical team, but most assessment can be done right on mom's chest. If baby is full term and healthy there is no reason to remove them from their parents. If mom is not doing well the baby can be held by the father.
When I attend births in hospitals, and sometimes even in out-of-hospital births, I see little advantage taken of this golden hour. There seems to be two reasons: interference from others and parents themselves not giving priority to this time.
Interference from outsiders
Very few things MUST be done within the first two hours. Contrary to popular belief, it is not usual for a baby to start nursing right away. They go through phases of being somewhat stunned to moving around more, to finding and mouthing the nipple, to finally suckling right around an hour after birth.
Pediatricians agree that newborns experience too much pain, as explained in a recent statement. I have seen hospital staff assure parents that baby will be able to nurse during shots only to give the injections before baby had latched for the first time. Now baby's experience at the beginning is pain instead of comfort.
Which procedures can wait? American Academy of Pediatrics concludes in their Sample Hospital Policy that vitamin K injections, weighing, eye antibiotics, measuring, and getting blood for newborn screening are all things that can wait. In fact, the earliest any of these needs to be done is 6 hours for the vitamin K injection. Some of these "standard" procedures can be delayed with benefits and certainly no drawbacks. Ask your health care provider how long you can safely wait for tests and medications.
Giving the golden hour priority
I know you want to let everyone you know about the amazing miracle that just occurred; your baby is here! But you will never get that time back. Grandma can wait to hear the news. Cousin Sam will hear all the details in a few hours. Please, I beg you, put your phone away. Stare at your baby. Murmur love into your spouse's ear because you both did an amazing job. Kiss. Hug. Take advantage of the birth hormones as much as you can. If you want pictures, have someone else quietly take them.
Right after birth the baby (unless he has narcotics in his system) will be alert and have his eyes open. This gives him a chance to get his first meal and meet his parents. Usually baby goes into a deep sleep around two hours after birth, and then would be a good time to contact the "outside world", take pictures, and sign paperwork. I just don't want anyone to miss out on that golden hour that only happens once in your baby's life!