Additive Manufacturing (AM) has been regarded as a technology with disruptive potential, offering the possibility of substantial reductions in the environmental footprint. The predominant approach to quantitatively evaluate AM’s environmental impacts relies heavily on the knowledge-intensive and time-consuming Life Cycle Assessment (LCA) methodology. To enable a faster design iteration cycle and alleviate the knowledge requirements of LCA modeling, the availability of an automated LCA tool could mark a remarkable leap forward in further enhancing AM's environmental performance. An emerging solution to achieve this goal is the combination of Machine Learning (ML) with LCA, the effectiveness of which has been initially demonstrated outside the AM domain. To explore the feasibility of predictive LCA for AM, this paper proposes a novel data-driven framework that integrates ML, product-process codesign, and LCA to support the environmental impact prediction of AM. The efficacy of the proposed methodology is demonstrated by taking the Fused Filament Fabrication (FFF) process as a case study. This work introduces three main contributions to the research community. First, a training dataset comprising 200 data entries, where each entry encompasses 5 design features, 7 process features, and 18 environmental impact categories is constructed. Second, through a two-stage process involving correlation analysis and an ML preliminary study, the initial 12 design-process parameters are refined to 7 key influential features. Lastly, the refined set of features and 7 different ML algorithms are employed to develop a data-driven LCA (DD-LCA) model for the FFF process. Notably, the Extreme Gradient Boosting (XGBoost) and Multi-Layer Perceptron (MLP) algorithms demonstrate good performance with a prediction accuracy of 98% and a root mean square error (RMSE) of 0.029. The developed model exhibits good generalizability when tested on new data. The paper concludes by addressing its limitations and outlining future research work.