I've put the word "problem" in quotation marks, because gun violence is not the actual problem. Gun violence is a symptom of a deeper problem in american society. And, the problem is NOT "the guns". Guns do not create the yearning that too many americans have to own and use them, any more than a pacifier creates an infant's desire to suck.
At the heart of the problem is the uniquely american obsession with the myth of "self reliance". The myth goes back further than the american west (unjustly glorified in too many TV shows and movies). It goes back to the "beginning" of the american story... 100 persecuted Puritans boarded a frail ship, navigated the treacherous North Atlantic, landing on Cape Cod, founded a colony. What self reliant folks those were. Uhhh no. They relied on the ship's crew, the ship's builder, each other, the indigenous people, the makers of the tools they brought, the land itself, and the whole enterprise was funded by the Virginia Company (that expected a substantial ROI)
Couple the belief in self reliance with zero sum thinking. This is the belief, fostered by the capitalist system, that in order to "win" someone else must "lose". The capitalist system uses zero sum thinking as a carrot and stick to rationalize working for poor wages to make someone else rich,and to justify huge inequalities. A lot of effort is put into indoctrinating children, who are born prosocial and feeling connected and connections. That is ripped away in favor of separation and choosing those who will lose so they will win.
What better way of being assured of winning than possessing a tool that is capable of quickly intimidating and killing so many losers, which is potentially anyone? For far too many americans, guns determine who will "win".