(1) Background: An important part of any neonatal hearing screening program is monitoring diagnostic visits to confirm or exclude the presence of hearing loss. In addition, time plays an important role in the diagnosis. We identified the number of children who came for a diagnostic visit and analyzed the time of the first audiological visit, depending on the result of the hearing screening test performed in the first days of a child’s life and the presence or absence of risk factors of hearing impairment. (2) Methods: We analyzed 6,580,524 children, of which 8.9% required further diagnostics. The mean time of follow-up diagnostic visit in the analyzed group was 130 days and differed due to the presence or absence of risk factors for hearing loss before and after the neonatal period. (3) Results: Although the risk of hearing loss in children with risk factors is 2.31 to 6.38 times higher than in children without risk factors depending on the result of the screening test, more than 40% of parents do not report to scheduled audiological visits. (4) Conclusions: Doctors, nurses, and midwives who screen hearing at the neonatological level play an important role in educating parents about the possibility of hearing loss in a child and the need for an audiological examination.