“Too many inquiries” is rarely impacting your credit score. If these inquiries do end up opening credit to you, that will have an impact (if suddenly you went from no credit to $50k). I cannot explain why the bank needs to run credit if you are securing the entire line of credit with cash money. Generally I have never seen/ experienced any situation where credit score/ report was not run when applying for credit. The best way to increase your credit score is to get the secured card and use it and pay it off every month. You can also build credit with car payments, utilities, store credit card, etc. You need to have credit history to have a credit score. Too little activity is not a good thing.

I was looking at Credit.com and saw some secured credit cards where credit checks aren’t done: