In the realm of quantum-effect devices and materials, two-dimensional electron gases (2DEGs) stand as fundamental structures that promise transformative technologies. However, the presence of impurities and defects in 2DEGs poses substantial challenges, impacting carrier mobility, conductivity, and quantum coherence time. To address this, we harness the power of scanning gate microscopy (SGM) and employ three distinct machine learning techniques to estimate the background potential of 2DEGs from SGM data: image-to-image translation using generative adversarial neural networks, cellular neural network, and evolutionary search. Our findings, despite data constraints, highlight the effectiveness of an evolutionary search algorithm in this context, offering a novel approach for defect analysis. This work not only advances our understanding of 2DEGs but also underscores the potential of machine learning in probing quantum materials, with implications for quantum computing and nanoelectronics.