This study was undertaken to develop a machine learning (ML) model to forecast initial seizure onset in neonatal hypoxic-ischemic encephalopathy (HIE) utilizing clinical and quantitative electroencephalogram (QEEG) features. We developed a gradient boosting ML model (Neo-GB) that utilizes clinical features and QEEG to forecast time-dependent seizure risk. Clinical variables included cord blood gas values, Apgar scores, gestational age at birth, postmenstrual age (PMA), postnatal age, and birth weight. QEEG features included statistical moments, spectral power, and recurrence quantification analysis (RQA) features. We trained and evaluated Neo-GB on a University of California, San Francisco (UCSF) neonatal HIE dataset, augmenting training with publicly available neonatal electroencephalogram (EEG) datasets from Cork University and Helsinki University Hospitals. We assessed the performance of Neo-GB at providing dynamic and static forecasts with diagnostic performance metrics and incident/dynamic area under the receiver operating characteristic curve (iAUC) analyses. Model explanations were performed to assess contributions of QEEG features and channels to model predictions. The UCSF dataset included 60 neonates with HIE (30 with seizures). In subject-level static forecasting at 30 min after EEG initiation, baseline Neo-GB without time-dependent features had an area under the receiver operating characteristic curve (AUROC) of .76 and Neo-GB with time-dependent features had an AUROC of .89. In time-dependent evaluation of the initial seizure onset within a 24-h seizure occurrence period, dynamic forecast with Neo-GB demonstrated median iAUC = .79 (interquartile range [IQR] .75-.82) and concordance index (C-index) = .82, whereas baseline static forecast at 30 min demonstrated median iAUC = .75 (IQR .72-.76) and C-index = .69. Model explanation analysis revealed that spectral power, PMA, RQA, and cord blood gas values made the strongest contributions in driving Neo-GB predictions. Within the most influential EEG channels, as the preictal period advanced toward eventual seizure, there was an upward trend in broadband spectral power. This study demonstrates an ML model that combines QEEG with clinical features to forecast time-dependent risk of initial seizure onset in neonatal HIE. Spectral power evolution is an early EEG marker of seizure risk in neonatal HIE.