  Molecular oxygen has been detected in the coma of comet
67P/Churyumov--Gerasimenko with a mean abundance of 3.80 $\pm$ 0.85\% by the
ROSINA mass spectrometer on board the Rosetta spacecraft. To account for the
presence of this species in comet 67P/Churyumov--Gerasimenko, it has been shown
that the radiolysis of ice grains precursors of comets is a viable mechanism in
low-density environments, such as molecular clouds. Here, we investigate the
alternative possibility that the icy grains present in the midplane of the
protosolar nebula were irradiated during their vertical transport between the
midplane and the upper layers over a large number of cycles, as a result of
turbulent mixing. Consequently, these grains spent a non-negligible fraction of
their lifetime in the disk's upper regions, where the irradiation by cosmic
rays was strong. To do so, we used a coupled disk-transport-irradiation model
to calculate the time evolution of the molecular oxygen abundance
radiolytically produced in ice grains. Our computations show that, even if a
significant fraction of the icy particles have followed a back and forth cycle
towards the upper layers of the disk over 10 million of years, a timespan far
exceeding the formation timescale of comet 67P/Churyumov--Gerasimenko, the
amount of produced molecular oxygen is at least two orders of magnitude lower
than the Rosetta observations. We conclude that the most likely scenario
remains the formation of molecular oxygen in low-density environments, such as
the presolar cloud, prior to the genesis of the protosolar nebula.
