The global transition to clean energy has been significantly supported by the steady increase in installed offshore wind capacity. Offshore wind energy generation is playing a critical role in this shift, with foundations serving as essential components for these installations. Traditionally, foundations have been driven into the seabed using impact-driven methods. However, more advanced installation techniques, such as vibratory installation, are gaining popularity due to their faster installation times and reduced underwater noise during the process. Despite its advantages, a deeper understanding of the factors influencing the vibratory installation method remains necessary. Numerical tools offer a promising approach for investigating these installation characteristics. In this work, we utilize the Convected Particle Domain Interpolation (CPDI) method, incorporating a two-phase extension, previously demonstrated to be effective in [1]. To capture the subsoil characteristics with greater accuracy, a multi-layered soil continuum is modeled, with data automatically derived from Cone Penetration Test (CPT) results collected at the installation site. The in-house code used in this study has been validated against full-scale monopile installations [2]. We present results from the vibratory installation of a full-scale monopile at the KASKASI-II wind farm. In addition to analyzing the installation characteristics, we explore the effects of installation frequency and hook-load on the process. We also compare the propagation of pressure waves through the seawater generated by the offshore structure during installation. This study provides valuable insights into the vibratory installation process, offering a comprehensive understanding of the installation dynamics and hydrodynamic effects in offshore wind energy projects.