Distant space target laser ranging encounters challenges due to the non-cooperative nature of the targets, resulting in nonlinear temporal variations in the echo signals. This nonlinearity poses a significant constraint on the performance of conventional Poisson methods. In response to this, the paper proposes a recognition methodology tailored for nonlinear laser ranging signals. In the realm of feature construction, a genetic algorithm is employed to intricately generate a set of mathematical features for the echo data, thereby substantially reducing the required number of training samples. Regarding model selection, a random forest model is adopted, successfully achieving the classification of signals and noise under the condition of expeditious training. The comprehensive analysis of simulation and measured data shows that the proposed method has better results, thus verifying its effectiveness.