Begin a policy of requiring prospective new and first time gun owners to require sponsorship, or a "buddy", from a current gun owner.
For the first five years, if that new gun owner commits a violent gun related crime, or that person's guns are involved in a such a crime without having been reported missing in a reasonable amount of time, then the "buddy" also bears legal responsibility for the crime.
After five years, the gun purchaser no longer needs a "buddy" and can sponsor new prospective gun owners as well.