Carotenuto et al. (Rheol Acta, 2021, 60, 309) recently showed that the complex viscosity of a Newtonian non-Brownian suspension is smaller than the steady shear one, whatever the imposed strain amplitude. Oscillatory shear can alter the microstructure through a shear induced particle diffusion mechanism. This mechanism needs time to show its effect and cannot be invoked to explain the observed mismatch between the steady shear and the complex viscosity. Moreover, in the limit of vanishing strain amplitudes and of very large ones, where the oscillatory shear is equivalent to consecutive steady flow reversals, the oscillatory shear should not alter the microstructure and the Cox-Merz rule should hold. With a combination of approaches exploiting the Lissajous-Bowditch plots, the Fourier transform rheology and the Sequence of Physical Processes, we investigate the microstructure changes induced in the first oscillatory cycles. The results from the different analyses agree with the microstructure rearranging mechanisms proposed by Carotenuto et al.: at small amplitudes, the oscillatory shear rotates couples of touching particles towards the flow direction, at medium amplitudes it breaks particle clusters and at very large amplitudes it reshuffles and reorients all the particles. We show that the vast majority of the microstructure rearrangement occurs soon after the flow inversion of the first cycle, while before it the microstructure is not altered. This allows us to suggest a procedure to "recover" the Cox-Merz rule: a single cycle of oscillation must be imposed and the stress response of the sole first quarter of oscillation must be analysed.