you can actually start adding positive history to your credit report. And there are certain places and services that you can use to report rent and utility payments to your report. They're not automatically included. Simple Bills, Experian Boost, and others will report some of those payments and help your credit.
There are also debit cards that will start reporting to credit bureaus as you use them. So there are a lot of options there. Also, don't discount raising your credit limit for an individual card. You can usually request a credit line increase. And of course, if your credit goes up and you aren't spending more money, that lowers your utilization and can have an impact.