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Waiting doesn't hurt, no. But 5/24 does. If it was me I would be willing to burn an inquiry (likely two because it's Chase) to find out. There have been some who bank with Chase that their first credit card was Freedom so they're not totally averse to thin files, they're averse to risky ones. A student card in and of itself isn't a bad thing. In fact they have a student version of Freedom - https://creditcards.chase.com/a1/freedom/student
Remember..... slow and steady wins the race. This is a marathon and not a sprint. So, I would take one of the Amex cards, I believe you said you prequalified for two of them, use it for 3-5 months, and let it report.
Then move to a second card, perhaps go with Chase at that time, but I might suggest going into a branch, opening a checking account and applying simultaneously. I'm not 100 % sure if it makes a difference, but I do believe it helps...
I would stay away from Cap 1, now, though you may get approved I believe there's no need for a triple pull so early with a thin file.......