E3 is absolutely the best way for Australians in my experience. It's more flexible than a H1B and the process is much simpler. The only downside is there is no simple path to a green card like H1B, but I managed to get one anyway.
You'd need a US entity to apply on your behalf. In my case they never asked about assets to pay the salary but that may be an issue.
https://www.uscis.gov/working-in-the-united-states/temporary...