Not as an enlisted soldier. If you posses a STEM related degree, you may be eligible for entry as a Specialist Service Officer. Check the Defence Jobs website for specific information.
Answered - Team Leader and Manager (Former Employee) - Sydney NSW
To become an General Service Officer there are only two methods, the Australian Defence Force Academy and the Royal Military College Duntroon.
Answered - General Service Officer (Former Employee) - Canberra ACT