Yes and No - It depends on a variety of factors.
Disclaimer: Thoughts/opinions/recommendations shared below are of my own; based on my experience living in Australia since the last 5.5 years.
1. What company/organisation are you talking about?
In most of the cases, permanent jobs literally mean that the job is permanent or on an ongoing basis (with some exceptions) and hence requires a person holding a permanent residency (PR) or a citizenship.
However, some retail compaines like Coles, Woolies, etc. offer permanent jobs for the frontline staff (e.g. service delivery roles like customer services, team member, etc.) who are on a temporary work visa. Their definition 'permanent' could be (in this scenario) "permanent shifts" - however eventually once your visa expires you'll be out of your job unfortunately.
For Federal/State government roles, they require a PR/citizenship holder. There may be some exceptions for State government roles but Federal role, they're very firm with the criteria.
Note: I was able to get a permanent job even though I was on my temporary visa. The organisation (non-government) gave me a conditional offer letter mentioning that until you're on a temporary work visa, your job is temporary with us (i.e. contract), and once you get your PR, your contract will be converted into a permanent role. It is a rare case though.
Recommendation: If you're applying for a permanent white collar job with a temporary visa chances are you won't get that job. So apply for temporary or contract roles instead - the probability of getting a temporary/contract role is high when compared to a permanent role (anyways there are a lot of temporary/contract jobs out there, you just need to find them tbh).
2. Duration of your visa/your length of stay?
If you have more than one year remaining on your work visa, you can still pursue the option of applying for permanent roles however, as I mentiond in the earlier point, the likelihood is very low. My recommendation would still be to same as mentioned in point 1.
3. Visa Condition/work rights
This is (kind of) a no brainer. If your visa allows you to work only part time, and you're applying for a full-time role, you cannot expect much out of it.
Tip: you need to be able clearly communicate to the employer about your working rights in Australia in a very simple yet explicit manner. Once an employer senses some complexity around your working rights, it will turn them off and they will prefer some other candidate with PR/citizenship or with less complexity. I will create a separate post to show how can you clearly communicate this.
In conclusion, my recommendation to you would be to give more preferance on temporary/contract roles, and if there aren't any left (which is less likely), then pursue permanent roles.
Super tip: It is always good to give a quick call to the hiring manager to introduce yourself, ask about the role, build some rapport with them, and then apply for the role (basically trying to sell yourself without sounding like a sales call) - your chances to getting a call for an interview increases.
I hope this helps - all the best.