Detecting stress and anxiety in speech has critical applications in education, mental health, and human–computer interaction. In this pilot study, we investigated the feasibility of automatically distinguishing public speaking–induced anxiety from neutral speech using a machine learning pipeline based on Mel-Frequency Cepstral Coefficients (MFCCs). Audio recordings from ten speakers, each lasting 4–6 min per condition (public speaking vs. private), were segmented into 5-s fragments, yielding 565 “solo” and 569 “public” segments. Following silence trimming, RMS normalization, pre-emphasis, and band-pass filtering (80–8 kHz), we extracted 13 MFCC coefficients (with Cepstral Mean & Variance Normalization) for each segment. A Gradient Boosting classifier trained on these features achieved an accuracy of 91.9% and F1-score of 0.918 in a stratified 80/20 train/test split, with per-class precision and recall around 0.92. Feature-importance analysis revealed MFCC9 (0.177), MFCC6 (0.160), and MFCC5 (0.145) as the most discriminative coefficients. These results demonstrate that, after rigorous signal cleaning, MFCC-based machine learning pipelines can reliably detect public speaking anxiety. Future work is planned to expand the dataset, incorporate delta-MFCC and spectral-contrast features, and explore deep learning on spectrogram images.