The main reason most openings are "Remote, US-only" is due to tax and labor laws.

By employing you, the US company must comply with all Australian tax and labor laws (in addition to the US laws). This is a huge burden. (Like the company must calculate and report how much revenue was generated through your work and pay Australian corporate income tax.)

Your best chance is to apply to US companies that already operate in Australia: they will have the necessary legal/HR infra set up. (For example Google probably has an office in Australia.)

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Another method may be to work as a contractor through a service like https://www.toptal.com (or even on your own if you can find contracts).