Studying multiple properties of a material concurrently is essential for obtaining a comprehensive understanding of its behavior and performance. However, this approach presents certain challenges. For instance, simultaneous examination of various properties often necessitates extensive experimental resources, thereby increasing the overall cost and time required for research. Furthermore, the pursuit of desirable properties for one application may conflict with those needed for another, leading to trade-off scenarios. In this study, we focused on investigating adhesive joint strength and elastic modulus, both crucial properties directly impacting adhesive behavior. To determine elastic modulus, we employed a non-destructive indentation method for converting hardness measurements. Additionally, we introduced a specimen apparatus preparation method to ensure the fabrication of smooth surfaces and homogeneous polymeric specimens, free from voids and bubbles. Our experiments utilized a commercially available bisphenol A-based epoxy resin in combination with a Poly(propylene glycol) curing agent. We generated an initial dataset comprising experimental results from 32 conditions, which served as input for training a machine learning model. Subsequently, we used this model to predict outcomes for a total of 256 conditions. To address the high deviation in prediction results, we implemented active learning approaches, achieving a 50% reduction in deviation while maintaining model accuracy. Through our analysis, we observed a trade-off boundary (Pareto frontier line) between adhesive joint strength and elastic modulus. Leveraging Bayesian optimization, we successfully identified experimental conditions that surpassed this boundary, yielding an adhesive joint strength of 25.2 MPa and an elastic modulus of 182.5 MPa.