Chase bankers in a retail branch can help you apply for a Chase freedom credit card if you can deposit at least US$10,000 into a Chase Savings account.

Similarly with Bank of America.

The credit line granted initially may be small but you will be able to request for a credit line increase by demonstrating your income level.

That first card will be reported to the credit agencies in about two months. Once that happened, you can apply for an US issued American Express card. You may still be declined by the computer due to your short credit history, however you can call for an manual review and convince the credit analyst to approve you base on your (presumably high?) income / asset.

There is no direct application for the Centurion card but you can apply for a Green/Gold/Platinum card and request for an Centurion invite after demonstrating significant spend.