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Just throwing in my experience. My BK was discharged in October and I'm on fire with rebuilding. I got a VS and OS through the SCT with low limits (250/750) and about a month after received preapprovals for both Ulta and Meijer (grocery store, also Comenity) in my email. I took both and both were soft pulls. Limits were again low (400/500) but I'm OK with that. I have store rewards for both so I'm pretty sure that's what triggered the pre-approvals. Incidentally, I don't spend a ton at Ulta, but I'm pretty consistent with shopping every few months. Credit scores were in the 660-670s when I got the preapprovals.
On the Mastercard or store card. I didnt get one yet but I just hit 6 months.