In ultrarelativistic heavy-ion collisions, a plasma of deconfined quarks and gluons is formed within 1 fm/c of the nuclei's impact. The complex dynamics of the collision before ≈1 fm/c is often described with parametric models, which affect the predictivity of calculations. In this work, we perform a systematic analysis of LHC measurements from Pb-Pb collisions, by combining an abinitio model of the early stage of the collisions with a hydrodynamic model of the plasma. We obtain state-of-the-art constraints on the shear and bulk viscosity of quark-gluon plasma. We mitigate the additional cost of the abinitio initial conditions by combining Bayesian model averaging with transfer learning, allowing us to account for important theoretical uncertainties in the hydrodynamics-to-hadron transition. We show that, despite the apparent strong constraints on the shear viscosity, metrics that balance the model's predictivity with its degree of agreement with data do not prefer a temperature-dependent specific shear viscosity over a constant value. We validate the model by comparing with discriminating observables not used in the calibration, finding excellent agreement.