Green manufacturing has become a pressing issue in recent years, driven by the acknowledgment of its long-term social and economic benefits, increasing demand for environmentally friendly products, and expanding regulations. One of the key approaches to attaining sustainability in green manufacturing is to design long-lasting products. Nevertheless, the traditional approaches have faced several unique challenges in designing a product with an extended lifetime, such as costly and time-consuming procedures, as well as the noisy, sparse, insufficient or incomplete data. This paper proposes a novel framework to tackle these issues from a data-driven perspective. Specifically, the proposed method employs Bayesian optimization with Monte-Carlo acquisition functions to take into account both product design factors and degradation signals and incorporate the inherent uncertainty in the modeling of underlying degradation processes and prediction of product lifetimes. A series of simulation studies are presented to assess the performance of the proposed method. A case study on the Lithium-ion battery dataset is further conducted, which demonstrates the advantages of the proposed method over existing benchmark approaches.