Autism spectrum disorder (ASD) has its origins in the atypical development of brain networks. Infants who are at high familial risk for, and later diagnosed with ASD, show atypical activity in multiple electroencephalography (EEG) oscillatory measures. However, infant-sibling studies are often constrained by small sample sizes. We used the International Infant EEG Data Integration Platform, a multi-site dataset with 432 participants, including 222 at high-risk for ASD, from whom repeated measurements of EEG were collected between the ages of 3-36 months. We applied a latent growth curve model to test whether familial risk status predicts developmental trajectories of spectral power across the first 3 years of life, and whether these trajectories predict ASD outcome. Change in spectral EEG power in all frequency bands occurred during the first 3 years of life. Familial risk, but not a later diagnosis of ASD, was associated with reduced power at 3 months, and a steeper developmental change between 3 and 36 months in nearly all absolute power bands. ASD outcome was not associated with absolute power intercept or slope. No associations were found between risk or outcome and relative power. This study applied an analytic approach not used in previous prospective biomarker studies of ASD, which was modeled to reflect the temporal relationship between genetic susceptibility, brain development, and ASD diagnosis. Trajectories of spectral power appear to be predicted by familial risk; however, spectral power does not predict diagnostic outcome above and beyond familial risk status. Discrepancies between current results and previous studies are discussed. LAY SUMMARY: Infants with an older sibling who is diagnosed with ASD are at increased risk of developing ASD themselves. This article tested whether EEG spectral power in the first year of life can predict whether these infants did or did not develop ASD.