  We posit a unified hydrodynamic and microscopic description of the
quark-gluon plasma (QGP) produced in ultrarelativistic $p$-Pb and Pb-Pb
collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV and evaluate our assertion using
Bayesian inference. Specifically, we model the dynamics of both collision
systems using initial conditions with parametric nucleon substructure, a
pre-equilibrium free-streaming stage, event-by-event viscous hydrodynamics, and
a microscopic hadronic afterburner. Free parameters of the model which describe
the initial state and QGP medium are then simultaneously calibrated to fit
charged particle yields, mean $p_T$, and flow cumulants. We argue that the
global agreement of the calibrated model with the experimental data strongly
supports the existence of hydrodynamic flow in small collision systems at
ultrarelativistic energies, and that the flow produced develops at length
scales smaller than a single proton. Posterior estimates for the model's input
parameters are obtained, and new insights into the temperature dependence of
the QGP transport coefficients and event-by-event structure of the proton are
discussed.
