There's nothing you can do. Nothing.

Even if you make the selling of guns completely illegal, how will that change anything? There are still tens of millions of guns in circulation in the USA. Many of them are family heirlooms.

The only (impossible) solution now is to buy people's guns off them by having cash-in stations, and that will be only partly affective and painfully expensive. Many will sit tight and refuse to hand them over. What then? You seize people's property? That would shake up the American social fabric so much it just wouldn't work. The political parties would feud over it and if anything you'd see the re-emergence of the Republican party as the governing power in the US for years on end.

The guns are a part of America now, and nothing you can do will change that. Perhaps over the course of decades (perhaps more than a century) you can influence things enough to steer people to a place where they don't see the point of guns any more, and just get rid of them, but that's hardly a quick fix. The guns are, heartbreakingly, here to stay.

Your best bet is education and proper healthcare for mental illnesses.