Accurate replication of statistical characteristics in synthetic datasets is critical for modeling, simulation, and decision-making in engineering and scientific domains. This study introduces a novel hybrid framework integrating the neural network concept for systematic parameter initialization and genetic algorithms for iterative optimization. The developed algorithm precisely replicates specified summary statistics, including mean, median, mode, standard deviation, minimum, and maximum. The proposed framework's novelty lies in its hybrid approach, ensuring robust applicability across diverse distributions such as Normal, Weibull, and Gumbel. For example, in generating a 2-parameter Weibull distribution, the framework accurately estimated shape, scale, and location parameters, achieving deviations of <0.1% from target values. This research bridges the gap between statistical accuracy and probabilistic realism in synthetic data generation. Its adaptability and computational efficiency make it suitable for advanced structural reliability, uncertainty quantification, and risk assessment applications.