An aim of autism spectrum disorder (ASD) research is to identify early biomarkers that inform ASD pathophysiology and expedite detection. Brain oscillations captured in electroencephalography (EEG) are thought to be disrupted as core ASD pathophysiology. We leverage longitudinal EEG power measurements from 3 to 36 months of age in infants at low- and high-risk for ASD to test how and when power distinguishes ASD risk and diagnosis by age 3-years. Power trajectories across the first year, second year, or first three years postnatally were submitted to data-driven modeling to differentiate ASD outcomes. Power dynamics during the first postnatal year best differentiate ASD diagnoses. Delta and gamma frequency power trajectories consistently distinguish infants with ASD diagnoses from others. There is also a developmental shift across timescales towards including higher-frequency power to differentiate outcomes. These findings reveal the importance of developmental timing and trajectory in understanding pathophysiology and classifying ASD outcomes.