Mass balance assessments of the East Antarctic ice sheet (EAIS) are highly sensitive to changes in firn thickness, causing substantial disagreement in estimates of its contribution to sea‐level. To better constrain the uncertainty in recent firn thickness changes, we develop an ensemble of 54 model scenarios of firn evolution between 1992‐2017. Using statistical emulation of firn‐densification models, we quantify the impact of firn compaction formulation, differing climatic forcing, and surface snow density on firn thickness evolution. At basin scales, the ensemble uncertainty in firn thickness change ranges between 0.2–1.0 cm yr‐1 (15–300% relative uncertainty), with the choice of climate forcing having the largest influence on the spread. Our results show the regions of the ice sheet where unexplained discrepancies exist between observed elevation changes and an extensive set of modelled firn thickness changes estimates, marking an important step towards more accurately constraining ice sheet mass balance.