I don’t think that US flight schools will sponsor a visa as an Australian
Look into it, but my understanding is that so long as you do the training with them (or FAA conversion of an existing license + instructor ratings), they will sponsor your employment you as an instructor up to at least the ATPL hours. Some of the visas for training also include a couple of years working rights post completion of your training.
This is pretty much what happens in Aus with uni degrees, international students come here, do their degree and are given a couple of years working rights on completion. That's usually enough for them to find either a longer term sponsor or start the permanent resident process.