(1) Background: In neonates and infants, the physiological modifications associated with language development are reflected in their Frequency Following Responses (FFRs) in the first few months of life. (2) Objective: This study aimed to test the FFRs of infants in the first 45 days of life in order to evaluate how auditory maturation affects the encoding of a speech syllable. (3) Method: In total, 80 healthy, normal-hearing infants, aged 3 to 45 days old, participated in this study. The sample was divided into three groups: GI, 38 neonates from 3 to 15 days; GII, 25 infants from 16 to 30 days; and GIII, 17 infants from 31 to 45 days. All participants underwent FFR testing. Results: With age, there was a decrease in the latency of all FFR waves, with statistically significant differences among the groups studied for waves V, A, E, F, and O. The mean amplitudes showed an increase, with a statistically significant difference only for wave V. The slope measure increased over the 45 days, with a statistically significant difference between GIII and GI and between GIII and GII. (4) Conclusions: The encoding of a speech sound changes with auditory maturation over the first 45 days of an infant’s life.