Coronary artery calcium (CAC) scoring plays a crucial role in the early detection and risk stratification of coronary artery disease (CAD). In this study, we focus on non-contrast coronary computed tomography angiography (CCTA) scans, which are commonly used for early calcification detection in clinical settings. To address the challenge of limited annotated data, we propose a radiomics-based pipeline that leverages pseudo-labeling to generate training labels, thereby eliminating the need for expert-defined segmentations. Additionally, we explore the use of pretrained foundation models, specifically CT-FM and RadImageNet, to extract image features, which are then used with traditional classifiers. We compare the performance of these deep learning features with that of radiomics features. Evaluation is conducted on a clinical CCTA dataset comprising 182 patients, where individuals are classified into two groups: zero versus non-zero calcium scores. We further investigate the impact of training on non-contrast datasets versus combined contrast and non-contrast datasets, with testing performed only on non contrast scans. Results show that radiomics-based models significantly outperform CNN-derived embeddings from foundation models (achieving 84% accuracy and p<0.05), despite the unavailability of expert annotations.