As an Australian living in Australia, how can I open a U.S. bank account without traveling there, or open any other international account?

You cannot. The new US (KYC) rules forbid anyone from opening an account in the US until and unless you are not physically present inside the bank branch. Do not fall for scams and schemes on the Internet that would tell you otherwise. You can shoot out an email to the largest banks in the US to small Community banks, and the answer will be the same. You have to be present in the US to be able to open a Checking/Savings accounts.