In my case, I too were not getting any pre-approved offers on the App. Amazon card was being extensively used. Thought of going for self-designed expression card, but didn't. Btw, currently I do not have any SB ac with them - earlier had 3-in-1 trading-demat-SB account - closed it around 15 yrs back.
Called their customer care n asked for core cards. I got Platinum card. No VKYC. No dox. Within 2 days got it. Then within 1 week, got Coral RuPay, LTF, thru pre-approved. Took it.
In June24, closed my Platinum Visa n opted for MMT Card, again thru pre-approved.
Currently, I have Amazon Visa, Coral RuPay n MakeMyTrip Visa Signature.
One core card n two co-branded cards. Very happy.