In this work, we present a trinification-based grand unified theory incorporating a global SU(3) family symmetry that after a spontaneous breaking leads to a left-right symmetric model. Already at the classical level, this model can accommodate the matter content and the quark Cabbibo mixing in the Standard Model (SM) with only one Yukawa coupling at the unification scale. Considering the minimal low-energy scenario with the least amount of light states, we show that the resulting effective theory enables dynamical breaking of its gauge group down to that of the SM by means of radiative corrections accounted for by the renormalisation group evolution at one loop. This result paves the way for a consistent explanation of the SM breaking scale and fermion mass hierarchies.