ill make it easy for you man.
The only way is to get a resident visa, either the following:
- J1 summer working program
- h1b or h2b business visa
- au pair visa...
etc...
all of those will get you a social security number. With that number in hand you can open a bank account asap.
Once you open the bank account you can pretty easily after about 4-5 months get a credit card thru the bank. Once you have that credit card you charge it for about 2 years... and then after that you apply for AMEX and you MIGHT(40% chance) get it depending on how you spent was...
Your history in Europe means squat here...
Based on personal experience... I went from 0 to 830+ on all 3 credit bureaus. A lot lower now because I have 3MM+ worth of miles from credit cards... : )
update: easiest visa to get is the J1. You apply and the chance to get is more than 90%. If your gender is F, then au pair is also a pretty easy one, and can find a job relatively easy... And tourist visa does NOT get you Social, so forget about coming here as a tourist.