Yes. I mean it really is as simple as that, yes, yes you can. You can get your first E3 Visa (or any renewals of visa) from inside OR outside of Australia. So why is this question asked so many times and why is there so much confusion? Can you get an E3 from a country other than Australia (for the first time?)
The main reason there is so much confusion is that there is a general recommendation from immigration attorneys that you should get your first visa in Australia.
Why do lawyers recommend getting your first E3 in Australia?
Well, the E3 visa is specifically for Australians, and therefore going into the US Consulate in Australia (Sydney, Melbourne OR Perth) will reliably be a safe place to go for someone to understand what is required for that visa.
If you go to a location outside of Australia, they are mostly (some aren't up to date) equipped to handle E3 visas, but some may not do them regularly, and some may have only ever done a handful at all. This will mean that there can be severe delays in processing and in some cases you may be rejected because they are not fully aware of what is required of you.
What is a Third Country National?
You are considered a “Third Country National” (TCN), as you are not from the country you are applying in, and you are not from the US. This will also mean that you are potentially pushed down the list and availabilities are not so open to you.
Do so at your own risk, but know that lots of people have done it before you!
Where can you get a visa from outside Australia?
For information on where to get your visa, you can use my review system! Every time someone completes their interview process they have the ability to write a review about how it went for them and I keep an aggregate score for all locations with reviews.
In Australia, you are from Australia, therefore not a TCN, so there should be more availabilities for appointments and the process will be more accurate and straight forward.
Best of luck with your application!