No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I would add that winning the lottery would only be necessary if the balances were really really high.
The Fico formula does not care about credit card limits only about utilization. For example someone with a $75 balance on a cc with a $100 limit is going to take a bigger score hit than someone with a $2500 balance on a $10,000 limit card. Everything else being equal.