Should it fall only on those descended from First Peoples to learn these languages? One could argue that settler Australians who acknowledge that they live on unceded First Nations land could do their part by learning and using some of the local language (and lore that goes with it).
Though with these languages being exclusively oral and unwritten, and post-settlement society depending extensively on writing, incorporating them in everyday life may be difficult. One could formulate orthographies and dictionaries for them, but then one would arguably have a constructed language that’s more a fan fiction of the original language.