Whatever we are doing with gun safety, including many states dropping all permit and training requirements and all states adopting concealed carry over the last 20-30 years and fatal gun accidents have dropped to the lowest numbers ever, not just the lowest rate, the lowest number despite a much larger population and millions of guns sold annually and going from a handful of states allowing carry with a permit to all states allowing carry and many not even requiring a permit, fewer than 500 annually, so we are doing something amazingly well with gun safety.
But I also share your concern, that's why I support gun safety being taught to all Americans in school just like sex ed and drivers ed. Let's get accidents down to zero. When you look at actual cases of fatal accidents all too often it is criminals or their family members and obviously none of them have ever been taught gun safety. We owe it to our children to protect them from gun violence just like we do for STDs and stranger danger and drugs.