We present the first unbiased survey of neutral hydrogen absorption in the Small Magellanic Cloud. The survey utilises pilot neutral hydrogen observations with the Australian Square Kilometre Array Pathfinder telescope as part of the Galactic Australian Square Kilometre Array Pathfinder neutral hydrogen project whose dataset has been processed with the Galactic Australian Square Kilometre Array Pathfinder-HI absorption pipeline, also described here. This dataset provides absorption spectra towards 229 continuum sources, a 275% increase in the number of continuum sources previously published in the Small Magellanic Cloud region, as well as an improvement in the quality of absorption spectra over previous surveys of the Small Magellanic Cloud. Our unbiased view, combined with the closely matched beam size between emission and absorption, reveals a lower cold gas faction (11%) than the 2019 ATCA survey of the Small Magellanic Cloud and is more representative of the Small Magellanic Cloud as a whole. We also find that the optical depth varies greatly between the Small Magellanic Cloud’s bar and wing regions. In the bar we find that the optical depth is generally low (correction factor to the optically thin column density assumption of $\mathcal{R}_{\mathrm{HI}} \sim 1.04$ ) but increases linearly with column density. In the wing however, there is a wide scatter in optical depth despite a tighter range of column densities.