American Express: transfer credit from Australia to the US

[Lance Luvaul]

Hi all, trying to build my credit history back up in the US after leaving and (stupidly) closing all of my accounts years ago.  Recently, I've gotten my US-based parents (with great credit history) to add me as an Authorized User on their US-based credit card account.  I also just got (days ago) approved for an Australian AMEX card using my established good credit history here (I live in Australia).

Now I want to use American Express's service where they facilitate an application for credit in a new country (the US in my case) using one's established credit in one's home country (Australia for me).  But as the approval was only days ago, should I wait a few months or do it straight away?  The hard-pull of my credit record AMEX performed will have knocked my score down slightly, but my history in Australia is extensive (and very good).

Does anyone have any experience with this AMEX process, and have any advice as to how to proceed / how long to wait / etc?