Surface radio antenna-based measurements of cosmic-ray air showers present significant computational challenges in accurately reconstructing physics observables, in particular, the depth of shower maximum, X$_{max}$. State-of-the-art template fitting methods rely on extensive simulation libraries, limiting scalability. This work introduces a technique utilizing graph neural networks to reconstruct key air-shower parameters, in particular, direction and shower-core, energy, and X$_{max}$. For training and testing of the networks, we use a CoREAS simulation library made for a future enhancement of IceCube’s surface array with radio antennas. The neural networks provide a scalable framework for large-scale data analysis for next-generation astroparticle observatories, such as IceCube-Gen2.