To address the time-domain inversion problem of vibration responses of a simply supported rectangular plate, this paper first expresses the time-domain dynamic load at each time instant as a series of two-dimensional Legendre orthogonal polynomials, thereby transforming the complex load field into an identification problem of a finite number of coefficients. The vibration response of the thin plate is then decomposed into a linear superposition of modal displacements, and a time-domain transfer relationship between modal forces and modal displacements is established based on the modal superposition principle, thereby achieving a coupled mapping between the displacement response at any spatial point and the dynamic load at each time instant. On this basis, an iterative regularization method based on the least squares QR (LSQR) algorithm is adopted to solve the inversion problem, effectively overcoming the numerical instability caused by the ill-conditioned nature of the system. In this paper, spherical and planar distributed dynamic loads are separately inverted. The spatial and temporal distribution characteristics of the obtained dynamic loads are highly consistent with those of the original input loads, verifying the effectiveness of the proposed method. By introducing the signal-to-noise ratio (SNR) parameter, the spherical dynamic load is inverted under Gaussian white noise with an SNR of 30 dB, and the method is found to have good noise resistance and identification accuracy. In summary, the combination of two-dimensional Legendre orthogonal polynomials and the iterative regularization method has high feasibility and engineering application potential in time-domain dynamic load identification.