We present the first results for the dust-scattering rings of GRB 221009A, coined as the GRB of the century, as observed by the Neil Gehrels Swift satellite. We perform analysis of both time resolved observations and stacked data. The former approach enable us to study the expansion of the most prominent rings, associate their origin with the prompt X-ray emission of the GRB and determine the location of the dust layers. The stacked radial profiles increase the signal-to-noise ratio of the data and allows detection of fainter and overlapping peaks in the angular profile. We find a total of 16 dust concentrations (with hints of even more) that span about 15 kpc in depth and could be responsible for the highly structured X-ray angular profiles. By comparing the relative scattered fluxes of the five most prominent rings we show that the layer with the largest amount of dust is located at about 0.44 kpc away from us. We finally compare the location of the dust layers with results from experiments that study the 3D structure of our Galaxy via extinction or CO radio observations, and highlight the complementarity of dust X-ray tomography to these approaches.