As a non-native English speaker who sought to speak English with an Australian accent after arriving in Australia, I would suggest the following:
- Interact with native Australian English speakers on a regular basis: Getting used to spoken Australian English, including pronunciation and accent is essential if you wish to talk like a native Australian and increased exposure to Australian English in real life will definitely assist you with this.
- Start developing your own spoken Australian English: In addition to direct exposure, it is important that you put in the necessary amount of effort to speak English with an Australian accent. Doing so constitutes a process characterised by gradual improvement, as you may find that your accent may not be as accurate as you would like it to be initially, although it will certainly improve the more you practise.
- Watch YouTube videos targeting Australian English: Although a rather basic step towards attaining your objective, such videos can enrich your knowledge of Australian English, including slang and other terms/expressions unique to Australian English. This can in turn assist you in improving your spoken Australian English as you begin to incorporate commonly used words/expressions into your everyday spoken English, while simultaneously improving your pronunciation.
In my experience, Australian English was fairly daunting mainly because of the peculiar accent, especially since American English was the accent I was mostly used to. This meant that understanding spoken Australian English alone took me approximately two to three months. Once I was able to fully understand it, I started to gradually improve my own English and, in the span of two years, finally succeeded at transitioning from an obviously foreign-sounding accent, to genuine Australian English.
I hope this helps!