Hot Rod didn't eat his puppy food when he was a baby, but did when we had a 2nd puppy and he was adult.
It really will not hurt the puppy to eat adult food, for the most part, but the puppy needs the extra vitamins and fat that are in puppy foods. So having said that, adults should not eat the puppy food because of the vitamins and fats.
There are all stage foods that might work for you. They didn't help me mine didn't care for them. One that comes to mind is Canidae. There are several others. Check out the health and diet forum.