I dont know if i have been blocked or as some people call it 'Dr Ralph'd'!Why's that? Has Amex Blocked you due to "Churning"? Once you get to :yes" with Amex AU, I think you'll need to hold got at least 6 months before you can do a Global Transfer to the US.
I think you're right then, have to look to non-Amex but you may need to go via a "secured" card first to build up your credit profile before you can go for a rewards credit card like one of the Chase ones. I'm not sure which bank will let you open a secured card from AU. Others who follow this thread may have DPs. That otherwise might be your first objective for your upcoming US trip. I would set up a checking account with Chase in branch and start the relationship with Chase that way. I don't think Chase offer secured cards but there are other banks who do and that may be the best way to get into the US card ecosystem in the first instance. Then you eventually have that bank as well as Chase - they say it's always good to have 2 in case one gets shut down. YMMV.
I had a plat charge card for a couple of years until 2023. Held a few other cards here and there since. Last year i hadnt applied for any cards until Sept when i went for the Velocity Platinum, got rejected with the 'we will send a letter in 5-10 days'. Then in December i got the HSBC Star Alliance card no worries. Went back today and had another crack at the Velocity Platinum and it did ask me to upload payslips but then said they will get back to me in 5-10 days so im pretty sure thats another no.
Anyway i will take on board the advice here and might go for a bit of a walkabout in the USA later in year trying to open bank accounts and let you know how i go!
