The Verdict: Not eligible
The ADF route is closed to you for now, because it starts from permanent residence. Look at skilled migration or a partner visa to become a permanent resident first.
Non-citizens can serve only as permanent residents, or New Zealand citizens on a Special Category visa, who have lived in Australia for a year. Service follows residence; it does not lead to it.
The main ways to permanent residence are points-tested skilled migration, employer sponsorship and, if your partner is an Australian citizen or permanent resident, a partner visa. If a parent was an Australian citizen when you were born, check citizenship by descent first: you may already have a claim.