It doesn't seem like either USyd or UNSW offer degrees specifically targeting paramedicine, but it does seem like both universities offer degrees that are somehow related to paramedicine:
UNSW's Bachelor of Medical Science provides the basis for a career in biomedical research and is also an appropriate first degree if you’re planning to progress to graduate medical or paramedical degrees.
Discover the science that underpins medical practice with a Bachelor of Medical Science. Develop an extensive understanding of the human body at UNSW Sydney.
www.unsw.edu.au
USyd's Bachelor of Science gives you the essential foundation for a career in healthcare or research, i.e. whether you want to join the leading edge of medical research or become a doctor or dentist with further study.
Our Bachelor of Science course opens up a world of opportunity and lets you to choose from over 40 majors.
www.sydney.edu.au
According to the Australian Paramedical College, registration of paramedics became legislated as of 2018, meaning that in order to become a paramedic in NSW (as well as other states), you will need a degree that focuses on paramedicine.
A career with NSW Ambulance is rewarding. Read this blog to explore how you can work with NSW Ambulance before gaining a university degree.
apcollege.edu.au
For a degree with a direct focus on paramedicine, you should consider CSU's Bachelor of Paramedicine or Bachelor of Paramedicine (Honours) as well as WSU's Bachelor of Health Science (Paramedicine).
Our Bachelor of Paramedicine is a NSW paramedicine degree accredited by the Council of Ambulance Authorities. Study your paramedic course online or on campus.
study.csu.edu.au
www.csu.edu.au
Western’s Bachelor of Paramedicine degree gives you the skills and knowledge you need to be a paramedic and play an integral role in the health system.
www.westernsydney.edu.au
I hope this helps!