We theoretically develop a machine-learning-based method for inferring the random onsite-energy fluctuations in disordered 2D generalized Hubbard models underlying spin-qubit platforms, using vision-based neural networks trained on tensor-network-generated charge-stability data. We investigate theoretically the feasibility of estimating the unknown disorder-induced chemical-potential fluctuations using simulated data generated from Hubbard-model-based charge stability diagrams of small 2D qubit arrays in the presence of random disorder. When all the Hubbard-model parameters are treated as unknowns because of the presence of random disorder, the onsite energy and onsite interaction are predictable with $R^2>0.90$ and $R^2>0.97$, respectively, for both the $3\times 3$ and $5\times 5$ qubit arrays, from our machine-learning algorithm using only observables from a $3\times 3$ region centered on the target dot. Thus, the most relevant experimental parameter for tuning spin qubits, the onsite energy, can be inferred reliably even in the fully disordered setting for computationally challenging $5\times 5$ arrays, which are already beyond the size of current semiconductor-qubit experiments.