With the implementation of a low-energy trigger, the surface array of the IceCube Neutrino Observatory is able to record cosmic-ray induced air showers with a primary energy of a few hundred TeV. This extension of the energy range closes the gap between direct and indirect observations of primary cosmic rays and provides the potential to test the validity of hadronic interaction models in the sub-PeV regime. Composition analyses at IceCube highly benefit from its multi-detector design. Combining the measurement of the electromagnetic shower component and low-energy muons at the surface with the response of the in-ice array to the associated high-energy muons improves the directional reconstruction accuracy and opens unique possibilities to extract the primary particle's mass. In this contribution, a new methodical approach for the analysis of these low-energy air showers is presented, including techniques for the identification of coincident background in the in-ice detector and a machine learning model based on convolutional neural networks to determine the elemental composition. The achieved performance in primary mass discrimination and energy reconstruction of air-shower events is discussed.