This study presents a data-driven approach to quantify uncertainties in the quantities of interest (QoIs), i.e., electron density, plasma drifts, and neutral winds, in the ionosphere-thermosphere (IT) system due to varying solar wind parameters (drivers) during quiet conditions (Kp$<$4) and fixed solar radiation and lower atmospheric conditions representative of March 16th, 2013. Ensemble simulations of the coupled Whole Atmosphere Model with Ionosphere Plasmasphere Electrodynamics (WAM-IPE) driven by synthetic solar wind drivers generated through a multi-channel variational autoencoder (MCVAE) model are obtained. The means and variances of the QoIs, as well as the sensitivities of the QoIs with respect to the drivers, are estimated by applying the polynomial chaos expansion (PCE) technique. Our results highlight unique features of the IT system’s uncertainty: 1) the uncertainty of the IT system is larger during nighttime; 2) the spatial distributions of the uncertainty for electron density and zonal drift at fixed local times present 4 peaks in the evening sector which is associated with the low density regions of longitude structure of electron density; 3) the uncertainty of the equatorial electron density is highly correlated with the uncertainty of the zonal drift, especially in the evening sector, while it is weakly correlated with the vertical drift. A variance-based global sensitivity analysis is further conducted. Results suggest that the IMF Bz plays a dominant role in the uncertainty of the electron density when IMF Bz is 0 or southward, while the solar wind speed plays a dominant role when IMF Bz is northward.