The research on neural network (NN) based image compression has shown superior performance compared to classical compression frameworks. Unlike the hand-engineered transforms in the classical frameworks, NN-based models learn the non-linear transforms providing more compact bit representations, and achieve faster coding speed on parallel devices over their classical counterparts. Those properties evoked the attention of both scientific and industrial communities, resulting in the standardization activity JPEG-AI. The verification model for the standardization process of JPEG-AI is already in development and has surpassed the advanced VVC intra codec. To generate reconstructed images with the desired bits per pixel and assess the BD-rate performance of both the JPEG-AI verification model and VVC intra, bit rate matching is employed. However, the current state of the JPEG-AI verification model experiences significant slowdowns during bit rate matching, resulting in suboptimal performance due to an unsuitable model. The proposed methodology offers a gradual algorithmic optimization for matching bit rates, resulting in a fourfold acceleration and over 1% improvement in BD-rate at the base operation point. At the high operation point, the acceleration increases up to sixfold.