The Greater Caucasus (GC) Mountains within the central Arabia-Eurasia collision zone, are an archetypal example of a young collisional orogen. However, the mechanisms driving rock uplift and forming the topography of the range are controversial, with recent provocative suggestions that uplift of the western GC is strongly influenced by an isostatic response to slab detachment, whereas the eastern half has grown through shortening and crustal thickening. Testing this hypothesis is challenging because records of exhumation rates mostly come from the western GC, where slab detachment may have occurred. To address this data gap, we report 623 new, paired zircon U-Pb and (U-Th)/He ages from 7 different modern river sediments, spanning a ~400 km long gap in bedrock thermochronometer data. We synthesize these with prior bedrock thermochronometer data, recent catchment averaged 10Be cosmogenic exhumation rates, topographic analyses, structural observations, and plate reconstructions to evaluate the mechanisms growing the GC topography. We find no evidence of major differences in rates, timing of onset of cooling, or total amounts of exhumation across the possible slab edge, inconsistent with previous suggestions of heterogeneous drivers for exhumation along-strike. Comparison of exhumation across timescales highlight a potential acceleration, but one that appears to suggest a consistent northward shift of the locus of more rapid exhumation. Integration of these new datasets with simple models of orogenic growth suggest that the gross topography of the GC is explainable with traditional models of accretion, thickening, and uplift and does not require any additional slab-related mechanisms.