The emergence of supply chain due diligence laws and other regulations has increased firms' responsibility for sustainability controversies in their supply networks. The availability of scores indicating how exposed a firm is to sustainability controversies is limited, particularly for lower-tier suppliers. To address this issue, we propose a novel approach using a random forest regression model to predict these scores. Our sample comprises firms up to third-tier suppliers embedded in 291 complex supply networks. To predict scores for these firms, we use a comprehensive set of features including firm static, financial, operational, and network-based features. We find that incorporating network-based features significantly reduces the prediction error by 2.18% points. We highlight the importance of considering a firm's supply chain stakeholder environment when predicting its sustainability controversy score. By a set of robustness checks, we show that our results hold for alternative algorithms, different feature selection approaches, and varying levels of data winsorization. Additionally, we show that extending the dataset decreases the prediction error and that the model can be applied to related sustainability scores. Our results offer further insights for supply chain professionals and policymakers.