The durability of concrete materials with regard to shrinkage and cracking phenomena depends on the evolution of the poroelastic properties of cement paste. The ability of engineers to control the uncertainty of the percolation threshold and the evolution of the elastic modulus, the Biot-Willis parameter and the skeleton Biot modulus is a keypoint of design practices to minimize the vulnerability of concrete structures at early-age. This article presents the uncertainty propagation and the sensitivity analysis of a multiscale poromechanics-hydration numerical model for cement pastes of water-to-cement ratio between 0.35 and 0.70. The model provides poroelastic properties required to model the behavior of partially saturated aging cement pastes (\emph{e.g.} autogenous shrinkage) and it predicts the percolation threshold and the undrained elastic modulus in good agreement with experimental data. The development of a stochastic metamodel using polynomial chaos expansion allows to propagate the uncertainty characteristic of the kinetic parameters of hydration, the quantitative cement phase composition, the elastic moduli of elementary material phases and the morphological parameters of the microstructure. The propagation does not magnify the uncertainty of the single poroelastic properties although, their correlation may amplify the variability of the estimates obtained from poroelastic state equations of cement paste. In order to reduce the uncertainty of the percolation threshold and of the poroelastic properties at early-age, it is recommanded to improve the accuracy of the apparent activation energy of calcium aluminate and, later on, of the elastic modulus of low density calcium-sillicate-hydrate.