Since gluon fields do not appear apart from quarks, did gluon fields first appear during the quark epoch?

Big Bang cosmology and grand unification theories say that the strong force and the electroweak force separated during the electroweak epoch, i.e., $10^{-36}$ to $10^{-32}$ seconds after the Planck epoch. I also read some accounts that say the strong force fields and the electroweak fields separated during the same electroweak epoch. However, since gluon fields do not a appear apart from quarks, then I suppose gluon fields did not arise until the origin of quarks in the quark epoch, i.e., $10^{-12}$ to $10^{-6}$ seconds after the Planck epoch.

If this is the case, then I suppose the strong force separated from the electroweak force during the electroweak epoch; yet no strong force fields arose until the quark epoch. Has anybody proposed this model?