This paper proposes a data-driven attack strategy capable of circumventing sliding-window $\chi^{2}$ detectors in remote state estimation. The developed strategy is designed to operate based on only the intercepted output data from the plants, estimators, and anomaly detectors, without the knowledge of system parameters. Moreover, in scenarios where sufficient data has been collected before occurrence of attacks, the proposed strategy exhibits optimality among all feasible attack policies using the same historical information. Through simulations, the effectiveness of the data-driven strategy is verified, with the stealthiness sustained by consistent empirical alarm rates.