  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 $\approx 1$ 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 \emph{ab-initio} 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 ab-initio 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.
