A close friend of ours recently moved from Montréal to Wichita, Kansas. He had no U.S. credit history whatsoever but was able to easily get a U.S. Amex card once he got there.
American Express has a program for Amex card holders that move from one country to another country (any country where American Express conducts business). Therefore, obtaining a U.S. Amex card in the United States should be straightforward enough if you have a Canadian Amex card in Canada. Generally, the lack of U.S. credit history should not be a hindrance in getting a U.S. Amex card as long as you have a Canadian Amex card prior to moving.
After getting and using your new U.S. Amex card, you will start building a U.S. credit history, which will then allow you to apply for other bank credit cards and loans.
From the AMEX - Global Card Transfers Website:
http://www.americanexpress.com/global-card-transfers/"PACK PEACE-OF-MIND WHEN YOU MOVE ABROAD
Transfer your Card when you move abroad. American Express aims to make the transfer process as quick and painless as possible. As each country has different regulations, tell us where you're moving to so we can direct you to the appropriate country to faciliate this transfer. Let's get started."