In this paper, we consider real-time beamforming design for dynamic wireless environments with varying channels and different numbers of access points (APs) and users in cell-free systems. Specifically, a sum-rate maximization optimization problem is formulated for the beamforming design in dynamic wireless environments of cell-free systems. To efficiently solve it, a high-generalization network (HGNet) is proposed to adapt to the changing numbers of APs and users. Then, a high-generalization beamforming module is also designed in HGNet to extract the valuable features for the varying channels, and we theoretically prove that such a high-generalization beamforming module is able to reduce the upper bound of the generalization error. Subsequently, by online adaptively updating about 3% of the parameters of HGNet, an online adaptive updating (OAU) algorithm is proposed to enable the online adaptive real-time beamforming design for improving the sum rate. Numerical results demonstrate that the proposed HGNet with OAU algorithm achieves a higher sum rate with a lower computational cost on the order of milliseconds, thus realizing the real-time beamforming design for dynamic wireless environments in cell-free systems.