Is it possible to have asthma from birth and not know it until 14?

Yes. It is easy to miss and many doctors have little or no training in pediatric pulmonary medicine.
Yes. Either by never having an attack before 14, or by mistaking attacks for colds.
Yes. Unfortunately, as a pediatric uc/er doctor, I have seen countless numbers of kids who's asthma has been either missed or ignored. I reeducate the parents and make "diplomatic suggestions to the pcp's to "look into this".