Epilepsy, a severe neurological condition is marked by sharp waveforms known as spikes in electroencephalogram (EEG) signals. Prompt detection of these spikes is crucial for reducing accidental injuries and safeguarding the lives of epilepsy patients. This article proposes an innovative deep-learning approach for epileptic spike detection using Spike and Non-spike Deep Convolutional Neural Networks (SNSDeepNet). Our method utilizes CNNs alongside an adaptive Layer-wise Adaptive Moments (LAMB) optimizer to effectively extract relevant features from time-domain (TD) and frequency-domain (FD) representations of spike and non-spike signals. The adaptive LAMB optimizer enhances the training process and accelerates convergence compared to traditional optimizers. The proposed model is evaluated using EEG recordings from three datasets: the Children's Hospital Boston (CHB-MIT) dataset, the Siena Scalp EEG dataset (Physionet Siena Scalp EEG Database), and the Bonn EEG dataset from the University of Bonn. After pre-processing and applying a peak detection algorithm, we extract TD and FD features from the signals. Our model demonstrates impressive performance. The CHB-MIT dataset achieved an average accuracy of 99.69%, sensitivity of 99.68%, F1-score of 99.11%, and a false positive rate (FPR) of 0.02698. For the Siena dataset, the model achieved an accuracy of 99.62%, specificity of 99.04%, sensitivity of 99.93%, F1-score of 99.48%, and an FPR of 0.009208. The Bonn dataset achieved an average accuracy of 94.10%, specificity of 92.39%, sensitivity of 97.35%, and an FPR of 0.0764. These findings underscore the effectiveness of the proposed architecture in accurately identifying epileptic spikes, highlighting its potential to enhance epilepsy diagnosis and treatment.