A cow bonds with her calf in a matter of minutes after birth, and this is based on smell and licking to stimulate blood flow. So removing the calf at any stage is always going to be stressful.
The cow's first milk (colostrum) is now in demand as a special health food so it's important to get this removed from the cow as soon as possible. The calf can then be given an accurate feed of colostrum by a teat.
The other benefit of milking the cow out properly lessens the risk of bacterial infection from the environment, which includes the calf's mouth.
So the best practice at present is to remove the calf at birth which is less stressful for both cow and calf.
Finding the teat can be a hazardous task for a newborn calf, especially if it's mother is a heifer and has never had this experience. An old cow will stand still and encourage the calf to move to the rear by licking it's tail head, but a heifer may keep moving to face the calf licking its head so preventing it feeding.
Raw juicy navels need to be treated with iodine as early as possible after birth to prevent infections. An extra treatment the day after birth is a good idea too.