secured cc doesn't really help IMHO and honestly are more meant for those who have had really bad credit versus no credit history
If you've been here for a year and prior to that you were struggling now would be a good time to try..I don't think having a secured credit card would go against you or anything, I'm just very wary of them.
I've personally seen immigrants and those who come here to work for a few years get approved with a social security number..and it is possible to get approved without one, though very difficult and under special circumstances
But for those that got approved with social and little time in america it was not easy. They had to prove that they have a good income, and have a considerable amount in the bank (10k) to have special consideration done--this is through a big bank too--Chase. (Sapphire preferred, 5k, within less then 6 months of coming over from Europe)
If you have low income (less then 50k) or do not have enough saved (10k) then it still isn't impossible but it would take more time, about a year or two of bank records to prove that you can be responsible with your account (no overdrafts, no insufficient fees, no returned checks..hopefully a good healthy balance but not always necessary)
I helped a student who was getting rejected by everyone including capital one for students because she has no credit history, she has bank history of 2 yrs and it took time to approve, esp at her barista salary--but she got a no frills card (no points or rewards) BUT it is not a secured card, it's free, and it's from a major or prime lender that helps build credit
I would try banking with citi or chase that has credit cards that can do good--bank of america offer secured credit cards..not exactly someone I would consider game player in credit cards..but this is all based on my personal opinion