When does a pn junction diode start conducting current in forward bias?

From what I have studied so far, under forward bias the pn junction’s depletion layer and barrier potential are reduced. Then there is something called threshold voltage that keeps coming up and that voltage has the same value as barrier potential, example 0.6V for silicon diodes, does it imply that minimum external voltage should be equal to barrier potential to start the current? Because as I am seeing it, the barrier potential of a zero bias diode is an equilibrium state and if it disturbed the countering process should start simultaneously, i.e. current, as soon as we apply a forward bias the barrier is reduced and electrons and holes can start diffusing again?