There are so many different options for what you’re trying to achieve it’s a bit hard to give advice. When do you intend to fly? If it’s within the next 10 months, it’ll be very difficult to find a business flight to the Americas given not many award seats are released. Also, given you currently have no points, the cost of purchasing the points outright is going to be very expensive, and you should consider whether just buying a business ticket outright might work out cheaper. For example, buying enough AA points to do a return business from SYD>LAX would cost approximately $4100AUD and you wouldn’t earn any status credit or points.
Given you’re happy to fly economy for all flights other than Australia to the Americas, you can just buy them outright as it’ll be easier/cheaper than points. This means you’re looking for one of two flights: Australia - LAX; or Australia - South America. I’d also note you could fly Perth to Auckland as this would open up some of other flights, including an Auckland to Buenos Aires.
Given you don’t have any points and you want to purchase AA or Lifemiles (LM), you can use the following airlines/flights given the partnership arrangements:
- Australia > LAX
- AA points
- Qantas: MEL, SYD, BNE > LAX
- AA: SYD > LAX
- United: SYD, MEL > LAX
- Air NZ: AKL > LAX
- Australia > South America
- AA points
- Qantas: SYD > SCL (Santiago)
- LAN: SYD > AKL > SCL
- Air NZ: AKL > EZE (Buenos Aires)
Finding award seats on these flights is very competitive and not many seats are released. You often have to look either a year in advance, or get lucky when an airline randomly releases the seats a month before the flight. There is heaps of information on this website about how to search for these flights, so you should start your research there.
I would also note that internal one-way flights in South America are very expensive. For example, a one-way flight from Santiago to Bogota is about $1000. LAX to Bogota is around $700.