Brain networks are hypothesized to undergo significant changes over development, particularly during infancy. Thus, the aim of this study is to evaluate brain maturation in the first year of life in terms of electrophysiological (EEG) functional connectivity (FC). Whole-brain FC metrics (i.e., magnitude-squared coherence, phase lag index, and parameters derived from graph theory) were extracted, for multiple frequency bands, from baseline EEG data recorded from 146 typically developing infants at 6 (T6) and 12 (T12) months of age. Generalized linear mixed models were used to test for significant differences in the computed metrics considering time point and sex as fixed effects. Correlational analyses were performed to ascertain the potential relationship between FC and subjects’ cognitive and language level, assessed with the Bayley-III scale at 24 (T24) months of age. The results obtained highlighted an increased FC, for all the analyzed frequency bands, at T12 with respect to T6. Correlational analyses yielded evidence of the relationship between FC metrics at T12 and cognition. Despite some limitations, our study represents one of the first attempts to evaluate brain network evolution during the first year of life while accounting for correspondence between functional maturation and cognitive improvement.