Applying for jobs in Australia as an overseas applicant

In 2021, I completed a Master's degree at the University of Sydney as an international student. Unfortunately, although I was approved for a student visa in 2020, I did not make it to Australia due to travel restrictions at the time, and had to complete the degree fully remotely (based in my home country).
Since graduating, I have wanted to work in research in my field, preferably in Australia. In the job hunting process, I have faced a sort of catch-22 where I am required to have work rights in order to be considered for jobs overseas, and would need to have secured a job (/offer) in order to seek work rights. How can I untangle this if I strongly prefer to work in Australia? My master's degree was a 1.5 year program and I believe that made me ineligible for the temporary graduate visa (485), and in any case, it is coming up on 2 years since I graduated.
Do you have any advice for finding employers that would accept overseas applicants (with no exisiting work rights) for research roles? Are e.g. universities generally open to accepting an applicant who is not enrolled and would require visa sponsorship, over a current student, e.g. for a research assistant role? I also don't have much research experience (my degrees have been coursework-based), so the odds seem stacked against me, but I must start somewhere and would be thrilled to be offered entry-level research work/ internship.

Thank you for any advice! Please let me know if this should have been posted in Visas and Immigration.