Monitoring greenhouse gas emissions and evaluating national inventories require efficient, scalable, and reliable inference methods. Top-down approaches, combined with recent advances in satellite observations, provide new opportunities to evaluate emissions at continental and global scales. However, transport models used in these methods remain a key source of uncertainty: they are computationally expensive to run at scale, and their uncertainty is difficult to characterise. Artificial intelligence offers a dual opportunity to accelerate transport simulations and to quantify their associated uncertainty. We present an ensemble-based pipeline for estimating atmospheric transport "footprints", greenhouse gas mole fraction measurements, and their uncertainties using a graph neural network emulator of a Lagrangian Particle Dispersion Model (LPDM). The approach is demonstrated with GOSAT (Greenhouse Gases Observing Satellite) observations for Brazil in 2016. The emulator achieved a ~1000x speed-up over the NAME LPDM, while reproducing large-scale footprint structures. Ensembles were calculated to quantify absolute and relative uncertainty, revealing spatial correlations with prediction error. The results show that ensemble spread highlights low-confidence spatial and temporal predictions for both atmospheric transport footprints and methane mole fractions. While demonstrated here for an LPDM emulator, the approach could be applied more generally to atmospheric transport models, supporting uncertainty-aware greenhouse gas inversion systems and improving the robustness of satellite-based emissions monitoring. With further development, ensemble-based emulators could also help explore systematic LPDM errors, offering a computationally efficient pathway towards a more comprehensive uncertainty budget in greenhouse gas flux estimates.