Soil constitutive models have evolved significantly over the years, with more advanced models enabling a more realistic soil behavior representation. However, this advancement often leads to an increase in the number of constitutive model parameters. While parameters can be obtained through in-situ or laboratory tests, this study focuses on the latter. Parameter identification can be cumbersome, especially when dealing with several interacting parameters. Thus, this study compares two approaches to streamline the soil parameter identification process. In the context of data-driven geotechnics, constitutive model parameters are determined using machine learning, and optimization algorithms. This study focuses on identifying model parameters based on the results of a synthetic drained triaxial test. In conjunction with the optimization approach, a sensitivity study is conducted to quantify their influence on the stress-strain behavior in drained triaxial tests. Results from both approaches show strong agreement with the target values in this synthetic case study. Moreover, the results demonstrate that the strength of the machine learning approach lies in its time efficiency compared to the optimization approach, whereas the latter excels in its flexibility in obtaining various model parameters. The findings of this study highlight the capabilities of automated parameter identification approaches and promote the use of more advanced constitutive models.