Hi Mala,
I think if you have a place to stay for the first few weeks that would be a big help. It would give you a chance to set up a few viewings and find more perminant place to stay after getting a feel for the area and work out travel routes etc. I'm on a similar budget and managed to find somewhere within 4 days. Had to fit in a lot of viewings and was a bit rushed but I looked up rooms for rent on websites before my move to HK and pre-arranged many of the dates and times for viewings. It was easy to find places looking for room mates, a bit harder finding one that suited what I wanted. But my advice is have a clear idea of what kind of environment you want to live in, the location in regards to where you can afford verses commute to work. And to stay safe try to have someone with you when you go to viewings or at least have someone who knows where you are going and when you'll be back. Also make sure you can have a working phone, I didn't have a HK sim at first and so made trying to arrange meeting people difficult, plus I needed access to my map apps to find the apartments.
Im not sure what it's like in Sydney, but for me I had to keep reminding myself that here, people live in smaller spaces and it's the norm to live with lots of people and mix housing and business properties in the same buildings. It takes some adjusting but persevere and you'll adapt quickly. If there's anything else I can help with let me know