With less than 1% of the guns that we have in the USA (USA civilians have around 350 million guns), Canada tried a total gun registration program. It cost them several Billions of dollars (US) to set up and operate the program and in spite of their best effort and a far more cooperative public, the result was utterly useless. In the entire history of the program, not one gun-crime was ever "solved", not one criminal was ever convicted from tracking info. The database of gun-owners and guns was always largely out of date and every time they tried random audits it was determined that at best the database was 30% accurate.
In the USA with 350 million guns and a highly uncooperative public, any sort of gun registration program is going to be orders of magnitude more expensive and even less accurate.
The FBI cannot even keep track of tens of millions of convicted felons who are not allowed to possess any guns. The government has all the laws it needs, but at all levels, none of our law enforcement agencies or prosecutors actually bother to enforce the existing laws.
For example, the huge percentage of all gun sales require a Federal form 4473 to be filled out and submitted to the FBI. Even the Obama administration said there were millions of cases each year where known felons lied on this form in an attempt to purchase a gun. This is a Federal and Sate felony punishable by at least 5-15 years in prison. And yet, the Obama administration only even arrested a couple dozen of these felons and only a few were prosecuted.
We have all the laws ans systems we need, what we don't have is the law enforcement and prosecutors willing to actually enforce those laws.

Fix that and you will solve the huge bulk of the problem.