Sudden cardiac arrest (SCA) poses a significant health challenge, necessitating accurate predictions of neurological outcomes in comatose patients, where good outcomes are defined as the recovery of most cognitive functions. Electroencephalogram (EEG) serves as a valuable biomarker for monitoring neurological states due to its rich, time-dependent information. This study aims to predict neurological outcomes using early EEG data by employing a Transformer model, which leverages multi-headed attention to identify patterns in lengthy sequences such as hour-long EEG recordings. Unlike traditional methods that use subsampled EEG epochs, we utilize the entire EEG sequences, subdivided into time steps, allowing our model to capture detailed temporal patterns via the attention mechanism. Moreover, we trained our proposed model using each EEG recording as an individual data sample but evaluated our model through aggregated patient-wise predictions. This approach allows us to boost the data sample size. Our results demonstrate promising predictive performance, achieving an AUROC of 0.82 and AUPRC of 0.90 on the holdout test set and an AUROC of 0.73 and AUPRC of 0.93 on an external test set with patient-wise predictions. This study highlights the potential of utilizing attention mechanisms to capture important time series progressions across EEG sequences for improving SCA prognosis.