Use P2P platforms where you’ll be talking to a person directly so you pay them the money and they send you to the bitcoin and vice versa. I don’t know in Australia but in my country we have e-wallets that are not necessarily connected to banks. Though to use e-wallets, we still had to fill in KYC. But it’s less restrictive than banks, imo. We can just deposit money to these e-wallets in any convenience store.
We have different type of P2P platform out their which you can use to buy crypto, the one which are under centralized exchange which you need to pass KYC before you can be able to use it and those which are done through DEX and also under some centralized exchanges which don’t make use of KYC, if you make use of the ones that require KYC you are not doing it privately as your government can get what ever they want if they contact the exchange and they can connect everything back to you. If you want to do anything and hide your if identity and in private the best way is to use means that don’t require you to pass KYC.