In the present work, a novel micromechanical data-driven Machine Learning (ML) framework was proposed to characterize material parameters in bulk metallic glasses (BMGs) using nanoindentation simulations with Berkovich and spherical tips. A vast collection of data on material behavior in BMGs during nanoindentation was compiled, utilizing a series of Drucker-Prager model coefficients. The predictive model was constructed using a nested machine learning algorithm, which incorporated hyper-parameters tuning and a principal model. This nested configuration optimized the architecture of a deep neural network, acting as the key estimator for BMG material properties. The outcomes indicated that the ML model proficiently predicted critical material properties, including compressive yield strength, elastic modulus, flow stress ratio, and Poisson ratio. Notably, the ML model exhibited superior accuracy in predicting elastic modulus and compressive strength, suggesting a robust correlation with flexural elasticity and compressive strength. Furthermore, the study highlighted the significance of input feature weight functions, as they strongly influenced the ML model's performance. Each output target's dependence on the individual proportion of input features contributed to the model's adaptability in handling variations in material properties. Finally, the findings of this work contribute to a deeper understanding of the relationships between input features and material properties, facilitating improved predictions of BMG behavior.