If a person is born deaf or with a hearing loss, then it is called "congenital". In fact, the word "congenital" is applied for any condition that a child is born with.
Most children who are born with hearing loss are raised as hard of hearing. That is, they use speech and hearing for communication perhaps supplemented with speech reading. They probably will be fitted with hearing aids or in cases of more severe hearing loss, a Cochlear Implant. Children with more severe losses may also use Cued Speech, but still their primary language is a spoken language.
Children who are born deaf may be raised either as deaf (using speech and speechreading, or perhaps even Cued Speech) for communication) or as Deaf (using ASL for communication).
Until recently, parents often didn't discover that their child was born with a hearing loss or deafness until the child failed to learn to speak. By that time, critical time was lost in the child's language development period. More recently, most states have enacted laws requiring newborn hearing screening.
Learning at birth whether a child is deaf or hard of hearing can help parents consider the alternatives for helping the child deal with the hearing loss or deafness.
See also Prelingual.