Whoever is interested, I can recommend the following:
Receive a SSN (if you don't have one already) for example during studies or internships with a J1 Visa
Get a mailbox service in the US (preferably in a not so seedy area -> away from the airports), places like UPS Shop offer a real street address.
Then it get's a little difficult, you have to establish a basic credit score.
You could apply in Australia for American Express and after using that account for a while request a global transfer to a US Account.
Alternatively you could receive a secured credit card issued by many financial institutions to establish the score. Means you do a term deposit of 2000 USD and get a card with 1000 USD limit.
After spending money and paying off you bills monthly you should have a decent score after ~ 6 months time. You can do a test if it's good enough for example to receive a consumer account for a Macy*s card.
Having just come back from a couple of years living in the US, I can offer the following advice vis-a-vis getting a decent US credit score, having been through the insanity of the US credit system myself (though coming out on the other side with a couple of 100k point Chase BA Visa bonuses, amongst others
).
Firstly, it will take you more like 9-12 months to have a decent score. There were several of us Aussie expats there at the same time and we all followed basically the same process (deposit-based "secured" credit card), except some started applying for unsecured cards after 6 months and some after 12. Most of the people applying at 6 months were declined, pretty much everyone applying at 12 months was approved (with ca. $15k+ credit limits - once you're in, you're in).
Secondly, you need to use the card, and pay it off, frequently. One of the differences we noted was that people who just sat on their cards and didn't use them, still had a relatively cough score after 6 months. People who used them had a better score. People who used them and made card payments every 1-2 weeks had the best scores.
Thirdly, you may struggle to be approved for decent cards without a local job, especially with a short (<5 year) credit history, as you will likely be asked to provide proof of income - and to the US system, nothing that happens outside of America counts.
Finally, *never* close that first secured credit card, or at the very least never close the first unsecured card. The length of your credit history is a big factor in how creditworthiness is calculated, and if you close that first card you effectively throw away the first 6-12 months of it.
So, my overall strategy were I to start again from scratch would be:
1. Get a secured credit card and start using it regularly, making payments to it at least once a month, preferably twice a month.
2. At the ~9 month mark, try for a store card (eg: Macy's), an Amazon Visa card, or a card from one of the "we specialise in bad credit" mobs like Capital One. Start using this card instead of the secured card, but in the same way (ie: frequent payments)
3. At the 12 month mark, start looking around for a decent "real" card with a signup bonus, and give it a go. The big risk you run is being asked to provide proof of income. You might need to start with less attractive signup-bonus cards (say, 10-20k points with US Airways or AA) and use them for another year before moving onto the really good ones.