I want to make it to American PE from Australia. What's my game plan?

Hello everyone!I'm a US citizen doing my undergrad in Australia and want to move back to the US at some point in the future to pursue a career in PE. Obviously, my geographic location poses some hurdles - Australian IB analysts at BBs typically don't move over to the US for 2-3 years, coming in as either a 3rd year analyst or 1st year associate. My understanding is that this will pretty much disqualify me from the typical on-cycle recruiting timeline that most analysts in the US go through. As such, I wanted to reach out to get some thoughts on what my plan of action should be.
Obviously, there's the basic path of landing an IB role here, transferring to the USA ASAP into 3rd year analyst and trying to land a seat from there. I spoke to a connection who had done something similar, transferring into a BB's NYC office as a 3rd year analyst and then moving into asset management, so I suppose it's not impossible. That's the only anecdotal information I have about that pathway though, so it might be harder than I think.There's also the difference in international rankings to consider too. Here in Australia, I believe Jefferies is our top shop for Sponsors, whereas in the US its JPM or BofA? If this is incongruous, should I select a bank based on it's American or Australian LevFin performance? Does it even matter?The other potential path is recruiting for PE as a graduate here in Australia for firms with an international presence. Blackstone has recruited seniors for their RE arm here, Bain recruits seniors for consulting (who place well in Bain Cap), and I'm sure there are others that I'm forgetting. Could landing a position her (either as a graduate or after a brief stint in banking) and then moving to the US as a lateral hire be a better method than the IB transfer?Sorry if this was a bit incoherent! I'm trying to get my thoughts in order now that the recruiting period is starting to ramp up.