An Impact Time and Angle Control Guidance (ITACG) problem with constraints on maximum lateral acceleration is investigated in this paper. The goal for this problem is to achieve precise interception of a stationary target at the desired impact time and angle, while considering the maximum lateral acceleration constraint during the guidance process. The previous ITACG methods generally struggled to handle a large initial heading error, severely limiting the guidance law's application scenarios. To tackle this problem and account for the maximum lateral acceleration constraint, an ITACG strategy is proposed from the perspectives of optimal guidance trajectory design and trajectory tracking in this paper. First, a guidance model is formulated, where Bézier curves are used to fit the guidance trajectory, and by parameterizing these curves and analyzing the trajectory constraints in detail, the optimal guidance trajectory design problem is transformed into an optimization problem of the control parameters. Then, a multi-layer zeroth-order Adam trajectory optimization algorithm is introduced to determine the control parameters without relying on gradient information. Subsequently, a hyperbolic tangent vector field trajectory tracking guidance algorithm is proposed to follow the pre-designed trajectory accurately. Finally, numerical simulations and equivalent physical experiments verify the effectiveness of the proposed guidance strategy.