From soft polymeric gels to hardened cement paste, amorphous solids under constant load exhibit a pronounced time-dependent deformation called creep. The microscopic mechanism of such a phenomenon is poorly understood and constitutes a significant challenge in densely packed and chemically reactive granular systems. Both features are prominently present in hydrating cement pastes composed of calcium silicate hydrate (C-S-H) nanoparticles, whose packing density increases as a function of time, while cements hydration is taking place. Performing nano-indentation tests and porosity measurements on a large collection of samples at various hydration degrees, we show that the creep response of hydrating cement paste is mainly controlled by the inter-particle distance, and results from slippage between (C-S-H) nanoparticles. Our findings, which pave the way for the design of concrete with improved creep resistance, provide a unique insight into the microscopic mechanism underpinning the creep response in aging granular materials.