The development of neural circuits over the first years of life has long-lasting effects on brain function, yet our understanding of early circuit development in humans remains limited. Here, aperiodic and periodic EEG power features were examined from longitudinal EEGs collected from 592 healthy 2-44 month-old infants, revealing age-dependent nonlinear changes suggestive of distinct milestones in early brain maturation. Consistent with the transient developmental progression of thalamocortical circuitry, we observe the presence and then absence of periodic alpha and high beta peaks across the three-year period, as well as the emergence of a low beta peak (12-20Hz) after six months of age. We present preliminary evidence that the emergence of the low beta peak is associated with thalamocortical connectivity sufficient for anesthesia-induced alpha coherence. Together, these findings suggest that early age-dependent changes in alpha and beta periodic peaks may reflect the state of thalamocortical network development.