Prestack seismic inversion serves as a bridge connecting seismic observations to subsurface rock properties, enabling quantitative estimation of elastic parameters, such as P-wave velocity (Vp), S-wave velocity (Vs), and density (ρ), which provides direct evidence for reservoir prediction and fluid identification. However, simultaneously inverting Vp, Vs, and ρ from prestack data is a highly nonlinear and ill-posed problem. Traditional inversion methods often struggle to achieve an optimal balance among accuracy, stability, and physical consistency. In recent years, deep learning has offered new insights through its powerful nonlinear mapping capabilities. However, purely data-driven models rely heavily on large labeled datasets and often overlook physical laws, leading to inversion results that lack geological consistency. To overcome these limitations, this paper proposes a multi-constraint two-step intelligent prestack inversion method. First, near-angle seismic data were used to robustly invert P-wave impedance (Ip). Then, employing TransUNet as the core network, a multi-constraint joint loss function was constructed to systematically integrate four types of prior information: (i) seismic data matching to ensure consistency with observed data. (ii) Physical relationship constraints linking Ip, Vp, and ρ. (iii) Empirical statistical relationships from well logs to regularize the ill-posed ρ inversion. (iv) Well data fitting to realize the matching of inversion results at well locations. This achieved high-precision inversion of Vp, Vs and ρ under the dual guidance of data driving and physical mechanisms. Tests on the Marmousi 2 model and actual shale reservoir data from the Junggar Basin demonstrated that the proposed method significantly improved inversion accuracy, stability, and noise resistance for all three parameters, particularly ρ, validating its potential for practical applications.