Current approaches to detecting depression and anxiety from speech primarily rely on machine learning techniques that utilize hand-engineered paralinguistic features and related acoustic descriptors derived from time- and frequency-domain representations of speech signals. Applying deep learning methods directly to raw speech signals has the potential to produce biomarker representations with substantially greater predictive power. However, these approaches typically require large volumes of carefully annotated data to learn robust and clinically meaningful representations of the underlying biomarkers. In this paper, we describe our efforts toward developing a deep learning model trained on a large-scale proprietary dataset comprising ~65,000 utterances collected from more than 23,000 subjects representative of relevant United States demographics. We present the techniques employed and analyze their impact on model performance. Our results demonstrate that the proposed models can extract content-agnostic biomarker information, which, when combined with lexical features extracted from audio, yields improved predictive performance in production settings. Our models are evaluated on ~5000 unique subjects and achieve performance of 71% in terms of sensitivity and specificity. To foster further research in mental health assessment from speech, we release the best-performing model described in this paper on HuggingFace.