Cleft lip and/or palate (CLP) is a prevalent congenital craniofacial anomaly that impairs normal speech articulation. Conventional clinical assessments such as nasoendoscopy and videofluoroscopy, while accurate, are invasive, costly, and require specialized expertise. This study introduces a non-invasive machine learning framework to distinguish between speakers with and without CLP using only acoustic features. Voice recordings from 100 participants (60 controls, 40 CLP) were collected following a standardized Spanish protocol targeting phonemes frequently affected by cleft conditions, including /k/ and /g/. Acoustic embeddings were extracted using the Spanish Wav2Vec 2.0 model, generating 772 features per sample. Supervised models like Support Vector Machines (SVM) and feedforward Neural Networks (NN) and unsupervised methods Gaussian Mixture Models (GMM), K-Means, and Spectral Clustering were implemented and compared. The SVM achieved the highest performance (F1-score = 0.93), followed by the NN (F1-score = 0.91) with improved sensitivity to CLP speech. Among unsupervised approaches, K-Means and GMM outperformed Spectral Clustering, particularly for the /k/ and /g/ phonemes. The /k/ phoneme yielded the highest discrimination (Accuracy = 0.86; ARI = 0.53), followed by /g/ (Accuracy = 0.73; ARI = 0.19). These findings demonstrate that acoustic embeddings effectively capture articulatory features distinctive of CLP, highlighting the discriminative relevance of velar stops /k/ and /g/. The proposed approach offers a scalable, non-invasive, and patient-friendly solution to support automated speech assessment and monitoring, particularly valuable in low-resource clinical settings.