False data injection attacks (FDIAs) are a real and latent threat in modern power systems networks due to the unprecedented integration of data acquisition systems. It is of utmost importance to understand attacking mechanisms to design countermeasures. To successfully deploy a FDIA, most past FDIA strategies need privileged power system information, which is carefully held by the power system operator. Newer approaches circumvent this issue by solely relying on intercepted measurement data, but they lack mathematical warranties of succeeding. This paper exposes power systems' vulnerability by showing that it is possible to deploy an attack without confidential information and, at the same time, to have a high probability of being successful. We present a scheme that learns (1) the implicit power system measurement distribution and (2) a surrogate of the unknown state estimator model. The proposed framework utilizes a Wasserstein generative adversarial network to learn the measurement distribution and an autoencoder to learn the unknown state estimator model. Additionally, we present a convergence proof that ensures that the proposed framework converges to the power system measurement distribution. The proposed method is demonstrated to be successful via extensive simulation on IEEE 9-, 14-, 57-, 118-, and 300-bus test cases.