Based on the relevant theoretical basis and research experience, this paper constructs a three-in-one, subjective and objective evaluation index system of inclusive preschool public service quality of “flexible”, “green” and “soft” quality. Subsequently, the GA-BP neural network quality assessment model based on machine learning algorithm was constructed by utilizing BP neural network analysis and hierarchical analysis to assign weights to the indicators. It was applied in a scientific operation process to synthesize subjective and objective data to understand the quality of public services of inclusive preschool education, and to propose an improvement path in combination with the IPA analysis model. The results show that the weights of the three first-level indicators are 0.428, 0.4231 and 0.1489, respectively, and the weights of the four second-level indicators, including special child care and migrant child care, are more than 0.1, while the weights of the other second-level indicators are all less than 0.1. Among the third-level indicators, the weights of the reasonable sharing of the cost of pre-school education among the government, families, kindergartens and the society, and the synergy of education and rehabilitation are more than 0.05, while the weights of the other third-level indicators are all less than 0.5, and the weights of the other third-level indicators are more than 0.1. In addition, the difference between the actual evaluation results and the simulation evaluation results of the teaching quality of universal preschool education public services is relatively small. And the error between the real values of GA-BP model is extremely small, and its average error is only 0.483.