Hello OP,
I have gone from green to gold to platinum without providing any tax return to Amex. I believe that Amex goes by your credit history with Amex and perhaps they pull a credit report.
If you do nothave an Amex now, just apply for a green card. Then after a year, and everything is A-OK, Amex should offer you a gold card. After after that, then it should be platinum.
If you have an existing card, somewhere on the amex website, there's a link that says something like "what other card are you eligible for?" That is how I found out that I was eligible for a platinum card.
Now, if I can only get THE black card just as easily....
Good luck!
David