Have you tried applying for an EB-2 NIW (National Interest Waiver) for experienced pilots,
O-1 for extraordinary ability, or
E-3 for Australians. While major airlines often require citizenship, regional airlines and specialized operators may sponsor visas due to shortages, but you must obtain FAA certification?
Netjets USA hires ...
https://www.netjets.com/en-us/netjet...ers-pilot-jobs