In a commercial dairy, the calves are removed from the cow at birth. This has many reasons, most of all ease of management. Some cows, especially first birth heifers, can take a stronger than normal attachment to the calf and "hide" milk. Some can even go as far as to not allow milking without the presence of the calf.
Here, we bottle feed Colostrum for 5 days then train the calves to drink milk, 2X/day, from a small bucket. This way we know exactly how much milk the calf is getting. We start our calves on pellet feed at 5 days and wean as soon as they are consuming 2 lb/day and 1 lb of hay, normaly 60-70 days.
In cases where the cow won't let milk down, rare with European breeds, 1/2ml of oxytocin fixes the problem. Talk to your vet. Retained milk can cause udder problems, excess milk for the calf can cause diarrhea.