Multi-agent market simulation is commonly used for testing trading strategies before deploying them to real-time trading. In electronic trading markets only the price or volume time series, that result from interaction of multiple market participants, are typically directly observable. Therefore, multi-agent market environments need to be calibrated so that the time series that result from interaction of simulated agents resemble historical -- which amounts to solving a highly complex large-scale optimization problem. In this paper, we propose a simple and efficient framework for calibrating multi-agent market simulator parameters from historical time series observations. First, we consider a novel concept of eligibility set to bypass the potential non-identifiability issue. Second, we generalize the two-sample Kolmogorov-Smirnov (K-S) test with Bonferroni correction to test the similarity between two high-dimensional time series distributions, which gives a simple yet effective distance metric between the time series sample sets. Third, we suggest using Bayesian optimization (BO) and trust-region BO (TuRBO) to minimize the aforementioned distance metric. Finally, we demonstrate the efficiency of our framework using numerical experiments.