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This paper proposes an automatic air-to-ground (A2G) channel model selection method based on machine learning (ML) using digital surface model (DSM) terrain data. In order to verify whether a communication network for a new non-terrestrial user service such as Urban Air Mobility (UAM) satisfies the required performance, it is necessary to perform a simulation reflecting the characteristics of the corresponding terrain environments as accurately as possible. For this simulation, A2G channel models corresponding to various terrain environments and a method of automatically classifying the terrain type of the simulation area must be provided. Many A2G channel models based on actual measurement results exist, but the practical automatic topography classification method still needs to be developed. This paper proposes the first practical automatic topography classification method using a two-step neural network-based classifier utilizing various geographic feature data as input. Since there is no open topography dataset to evaluate the accuracy of the proposed method, we built a new dataset for five topography classes that reflect the characteristics of Korea's topography, which is also a contribution of our study. The simulation results using the new data set show that the proposed ML-based method could increase the selection accuracy compared to the technique for direct classification by humans or the existing cross-correlation-based classification method. Since the proposed method utilizes the DSM data, open to the public, it can easily reflect the different terrain characteristics of each country. Therefore, the proposed method can be effectively used in the realistic performance evaluation of new non-terrestrial communication networks utilizing vast airspace such as UAM or 6G mobile communications. [ABSTRACT FROM AUTHOR]