Efficient simulation of photon registrations in single-photon LiDAR (SPL) is essential for applications such as depth estimation under high-flux conditions, where hardware dead time significantly distorts photon measurements. However, the conventional wisdom is computationally intensive due to their inherently sequential, photon-by-photon processing. In this paper, we propose a learning-based framework that accelerates the simulation process by modeling the photon count and directly predicting the photon registration probability density function (PDF) using an autoencoder (AE). Our method achieves high accuracy in estimating both the total number of registered photons and their temporal distribution, while substantially reducing simulation time. Extensive experiments validate the effectiveness and efficiency of our approach, highlighting its potential to enable fast and accurate SPL simulations for data-intensive imaging tasks in the high-flux regime.