In case people are still looking at this question, as at July 2024, there are a range of free maps available as GeoTIFF for download for Australia. Feel free to update this answer as the current state will no doubt change.
National
Geoscience Australia has many maps of various scales (1:50k, 1:100k, 1:250k, 1:1m) available as GeoTIFF for free download
https://www.ga.gov.au/scientific-topics/national-location-information/topographic-maps-data/topographic-maps
States
The level of free digital mapping available varies widely from state to state. Some areas of the states are reasonably well covered by free Geoscience Australia maps (eg the Kimberley, Cape York). In rough order of how useful and free the GeoTIFF/GeoPDF maps are by state (at 2024):
NSW
NSW Spatial Collaboration Portal has a wide range of maps of various scales (1:25k up to 1:100k) in both GeoTIFF and GeoPDF formats, for various years, available for free download:
https://portal.spatial.nsw.gov.au/portal/apps/webappviewer/index.html?id=06e3c2e0de1e4efda863854048c613c6
Queensland
Does not have GeoTIFF maps available. The QTopo service has free GeoPDF maps of various scales (1:10k up to 1:100k) that can be downloaded and converted to GeoTIFF using tools like GDAL.
https://qtopo.information.qld.gov.au/
Tasmania
TASMAP has a range of maps of various scales (1:25k up to 1:250k) in both GeoTIFF and GeoPDF formats available for purchase at a small cost (~$2 each)
https://nre.tas.gov.au/land-tasmania/tasmap
Victoria
Vicmap has a range of maps of various scales (1:25k up to 1:100k) in GeoPDF formats available for purchase at a cost (~$8.50 each)
https://vicmaptopo.land.vic.gov.au/
Western Australia
Landgate has a range of maps of various scales (1:25k, 1:50k, 1:100k) in locked GeoPDF format available for purchase at a cost (~$15 each). Due to locked format, not sure if these can be converted to GeoTIFF:
https://www.landgate.wa.gov.au/location-data-and-services/maps/topographic-maps/
South Australia
Currently does not have GeoTIFF/GeoPDF maps available
ACT
Covered by NSW
Northern Territory
Covered by Geoscience Australia maps