YES!!! LOL my daughter got up in the middle of the night last night and asked me to tell my husband to stop snoring because it scared her- she thought it was monsters. I told her it was Daisy, our pittie, and she said "Well tell her to stop it and be quiet!"
It is common, they are a "short-muzzle" breed. I didn't know that until I looked up taking dogs on airplanes, and they have certain restrictions with short muzzled dogs. AmStaffs were on the list!
BUT to be safe, make sure you are using an allergy-free puppy food, without corn, wheat, beef, and fillers because those are likely to cause allergies. You can also buy benadryl for dogs at pet stores, liver flavored to see if he has seasonal allergies!