With the explosive growth of mobile communication technology, the number of access terminals has increased dramatically, which will make the pilot contamination caused by pilot reuse extremely worse due to limited pilot resources. It is difficult to apply a traditional pilot assignment algorithm to serve the numerous access terminals simultaneously in real time with low complexity, so there is necessity to design a scalable pilot assignment scheme in the case of massive access. In this paper, we propose a scalable deep learning-based pilot assignment algorithm to maximize the sum spectral efficiency (SE) of cell-free large-scale distributed multiple-input multiple-output (MIMO) systems with massive access. The mapping between user locations and pilot assignment schemes is learned by a deep neural network (DNN). The training samples of the DNN are generated by a min-max algorithm, which minimizes the maximum interference to alleviate pilot contamination. The output of the pretrained DNN is used as the initial value of the min-max algorithm to achieve better pilot assignment schemes and reduce the algorithm complexity. The simulation results show that the proposed algorithm has better convergence with massive access and achieves a higher sum SE in near real time.