How does airfoil thickness affect the Mach number at which it experiences transonic flow?
The displacement effect causes the flow around a thick body to speed up more than around an equivalent but thinner body. The thicker body pushes the air aside and around itself more, causing the flow to accelerate relative to the vehicle and to become supersonic at a lower flight Mach number.

Wing sweep has a similar effect, as only the orthogonal speed component will be affected by the wing and the effective Mach number of all thickness-, camber- and angle-of-attack-related effects is reduced by the cosine of the sweep angle. Again, the displacement effect will be reduced by sweep.