To actually answer your question:
The most straightforward answer has already been posted by @StephenG - get a lawyer. It's probably cheaper in the long run and certainly much quicker and easier. Lawyers do this kind of thing all the time for all sorts of reasons - trust disbursements, will benefits, insurance payouts, property dividends, and so on, with a nontrivial amount of those either anonymous, confidential, or at least impenetrable to the common recipient.
- Several major bank ATMs, at least in capital cities, let you deposit into the ATM with just the BSB, Account number, and the depositor's mobile phone number (which could be fake, they have no way to know). If you can make multiple smaller deposits over time (none of them will accept close to the number of bills you're talking about all at once), this would work.
- You can set up a Trust. The Trustee of a trust can get a bank account in the name of a trust. You can then wind up the trust once you're done with it. There is nothing complicated about a trust, but it will take a small amount of research because it's going to be a pretty arcane system to a layman. In some states you may need to pay Stamp Duty to formalize a trust.
- If you're loaded and have a few months, you could buy real estate, sell it, and have the settlement include a payment instruction as a disbursement. The money will come from the account of the settlement agent or lawyer. It's totally traceable by various authorities, but won't be easily traceable by your friend.
- So, are you two loners who are only friends with each other? You don't have one mutual friend whom you could convince to transmit the money (by cash or electronic transaction) on your behalf, and swear not to tell?
- Convince your friend to set up a bitcoin wallet and ... well, it's not really anonymous so much as deniable.
- Grab an Uber to his house (ideally from a random street corner), and when you get there, tell the driver that you want to play a prank on your friend, and you'll pay him $50 to knock on the door and hand over this envelope with all these fake bills in it, I'll be hiding right over there so that I can film his reaction. Well, it would probably work - most rideshare drivers I've met are doing it as a second (or third) job and are always happy to get easy money like that.
- Or, even simpler, leave the cash-filled envelope in his mailbox? There is not really any risk if no-one, least of all your friend, expects it to be there.
Some quick notes:
In Australia, there is currently nothing illegal about dealing in cash (but the government is trying to change that... https://treasury.gov.au/policy-topics/economy/black-economy/cash-rules-2019). There is no requirement that a recipient has to be able to trace a payment - only that the authorities can. And you don't have to do anything to ensure that this is possible, only financial institutions have to have rules in place https://www.austrac.gov.au/business/legislation/amlctf-act (though it is illegal for you to deliberately deceive them to prevent this - and, no-one is going to make it easy for you to do legal things that look like or could potentially be illegal).
Part of those rules include that multiple regular smaller payments over time are to be treated with the same scrutiny as a single large one. Similarly, payments just under the threshold should be scrutinized the same as payments above the threshold. (If that sounds ambiguous and ripe for loophole abuse, you'd be right: https://www.austrac.gov.au/news-and-media/media-release/austrac-and-westpac-agree-penalty, https://www.austrac.gov.au/austrac-and-cba-agree-700m-penalty)
More importantly, as far as a non-cash transfer of any kind goes, I wouldn't try it myself. I know for sure that if I received any money I wasn't expecting and couldn't identify, I'd flag it with my bank as a mistaken transaction, and they'd retrieve it. Even if they couldn't actually return it to the depositor (such as for a cash deposit), it would still be surrendered to a bank holding account.
Also, you don't have to worry about tax implications for your friend. Cash gifts are not normally taxed as income (but interest earned on it is). Not being a charity simply means that you, the giver, cannot treat it as a deduction against your own tax (like you could if the recipient was an appropriately registered charity); it has nothing to do with paying tax, only with the inability to claim tax deductions. Though in principle, it is his obligation to prove to the ATO that it is not income if they ask (but in practice, him not knowing where it even came from is significant). People give gifts, shout each other drinks, place friendly bets, and all sorts of other things all the time. Simply because gifts are cash, even if they're anonymous, does not make them illegal - only if you try to frustrate regulatory efforts to trace your payment will you have problems. You are allowed to remain anonymous to a recipient, but not necessarily anyone else who helps to facilitate a transaction.
Setting up a business is overkill compared to setting up a trust, but a charity is even worse. The legal requirements for a charity are significant in Australia. But if it's your business, there's no reason that you can't operate it any way you want (in terms of whom you choose to make payments to for whatever reason). However, keep in mind that an ABN is not necessary but also definitely not sufficient for creating a business. ABNs are specifically for GST tax purposes and the "business" you've described (i.e. making one payment for nothing) wouldn't have either GST credits or GST debits, making it pointless. It also wouldn't help to hide your name, as you'd need a registered Business Name or Trading Name (https://asic.gov.au/for-business/registering-a-business-name/) to hide your own name, but that has a public register of the name of the business owner. A Private Company can be set up, but registration (https://asic.gov.au/for-business/registering-a-company/) is still with ASIC who, while they won't provide your ownership information for free on the internet, will provide an extract of registration to anyone who will pay a couple of dollars. Basically, you'd need someone (like an accountant or lawyer) to be substituted (in the correct legal fashion, and for a fee) if your purpose is to prevent casual inspection of the ownership of a business or partnership. In short, it's not a simple or cheap option to set up a business to make a single anonymous transaction.