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Any credit card companies that do soft pulls?
As a member, my recent approval with Amex was a SP, there was no HP for it . If you're not a cardholder with Amex already, anticipate a HP. If you are a cardholder with Amex, it goes without saying that YMMV so it's possible to receive a HP, but many here have gotten approved with no inquiry as current cardholders.
AMEX SP for current cardholders is very much YMMV.
I suspect that the OP can find examples of what they're looking for by performing a Google search on "Comenity shopping cart trick".
I feel obliged here to issue what has become a more-or-less standard warning to exercise great care when using the Comenity shopping cart trick. It's way too easy to load yourself down with lots of store cards with low limits for establishments that you'll likely never actually shop at, and Comenity has a nasty habit of AA (adverse action) against account holders that build up a lot of SCT cards, particularly if they get one of Comenity's co-branded major bank cards (e.g., the BJ's Perks MasterCard or the Williams-Sonoma Visa). So be very careful if you go that route, only get one or two cards for places that you actually shop at, take care that you don't have a lot of store cards before applying for one of their major bankcards, and so on.
OP - I do not think any CC will issue a card to a new customer w/o at least 1 HP.
You can certainly check out the "pre-approvals" for the bank/issuer - that is an SP if you are trying to gauge your chances.
There are links somewhere in these forums - but you can Google "Pre-Aproved Credit Cards" and lots of links pop up.....
I want to thank everyone who commented thus far, I am a little more educated about my approach and I will let you all know my results.
Your read was very helpful.