I’d like to share my experience of getting my Credit Card from American Express within one Month upon arrival in the United States.
Some Dates involved:
Arrival in Cleveland:   2 Aug
Go International Student Service to get my job letter:    15 Aug (after at least 10days) and Sesurity Office closed at 4, so  I waited till the next day.
Go Social Security Office to Apply SSN: 16 Aug
Get SSN Number:   17  Aug (Only Number; SSN card got 22 Aug)
Apply Credit Card: 17 Aug
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Blue Cash For Student . AmEx
Add tuition and fees plus fellwoship as "House Hold income"
Check Status (search "card application status") on 19<?> told me to verify "Billing Address" i had no phone, so waited till monday
Phoned AmEx to verify information they needed on 22 Aug.  APPROVED.
Sep 1st. Card Received by mail.
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Citibank Dividend Platium Select Card
Aug 30. Rejection by mail for no credit history. I should try " … for college student" hehe