Amplitude variation with incident angle (AVA) inversion for partial angle stack seismic data is an extension of acoustic impedance inversion. It adopts the P-wave reflection coefficient to link seismic amplitude information with elastic parameters and incident angle. This method generalizes conventional acoustic impedance inversion to pre-stack seismic data, enabling the effective inversion of multiple elastic parameters by utilizing seismic data acquired at different incident angles, such as angle gather data or partial angle stack data. This study addresses the limitations of commonly used AVA inversion with Cauchy regularization. Due to the nonlinearity of Cauchy regularization, the iterative re-weighted least squares algorithm is extensively employed. It has been shown that the accuracy of inversion results of this non-linear inversion algorithm is highly dependent on the initial solution. When geological conditions are complex, the initial solution must be close to the optimal solution to ensure accurate inversion results. To address this challenge, this study proposes combining the ensemble smoother with multiple data assimilation (ES-MDA) and AVA inversion with Cauchy sparse regularization. Specifically, the posterior mean of ES-MDA is used as the initial solution for AVA inversion with Cauchy sparse regularization. ES-MDA is a stochastic method that solves inverse problems by iteratively updating an ensemble of model realizations, yielding a solution that closely approximates the optimal solution. Practical application indicates that, compared with AVA inversion with Cauchy sparse regularization using a standard initial solution, the proposed method achieves improved accuracy in estimated elastic parameters. The research findings offer new technical approaches for seismic prediction with AVA inversion in complex reservoirs.