The geometry of the inner accretion flow in the hard and hard-intermediate states of X-ray binaries remains controversial. Using NICER observations of the black hole X-ray binary MAXI J1820+070 during the rising phase of its 2018 outburst, we study the evolution of the timing properties, in particular the characteristic variability frequencies of the prominent iron K$alpha$ line. Using frequency-resolved spectroscopy, we find that reflection occurs at large distances from the Comptonizing region in the bright hard state. During the hard- to soft transition, the variability properties suggest the reflector moves closer to the X-ray source. In parallel, the peak of the iron line shifts from 6.5 to ~7 keV, becoming consistent with that expected of from a highly inclined disc extending close to the black hole. We additionally find significant changes in the dependence of the root-mean-square (rms) variability on both energy and Fourier frequency as the source softens. The evolution of the rms-energy dependence, the line profile, and the timing properties of the iron line as traced by the frequency-resolved spectroscopy all support the picture of a truncated disc/inner flow geometry.