Welcome to the road and good for you for double-checking the rules! Yes—driving without shoes is technically legal in the United States. It’s up to individual state legislation, but so far, most states don’t even mention driving without shoes, let alone have laws against it.
Even people who are used to going through life without footwear should reconsider when they’re getting ready to operate a vehicle. You can always keep a pair of shoes in your car designated for driving, just maybe consider getting some air fresheners, too!