This can be accomplished by doing an NICS background check on each and every person and providing proof of pass/fail status. I would propose that this be done at the next renewal date for the person operators license or photo ID.
Privacy advocates would take issue with this. So would I. It's needlessly intrusive from the standpoint of those who have no interest in firearms ownership. Even if it didn't run afoul of the law, it would be wildly unpopular.
And yet again, why bother? We went for over two centuries without background checks. The NICS system hasn't been proven to reduce the number of guns in the hands of criminals, nor has it been shown to have any impact on crimes committed with guns.