A dog that fearful won't necessarily become a fear biter. They have to be cornered usually as the super scared ones almost always choose flight over fight. The socialization window has not closed. It never fully closes. The prime portion of socialization doesn't close for most pups till 5 months. There is still time it will just have to be extensive. Almost all your training energy must center around it.
It sounds like you bought from a breeder that doesn't socialize his pups at all.