Since there is no 'gun registry' in the USA,
So you say...I think an argument could be made that there is one. But at the moment, it is fractured, disjointed, not even remotely all inclusive or currently accurate. But that could be changed. All it takes is a law or two and some money.
First point, leaving aside, for the moment, those states that actually DO have a registration system, every gun that has passed through an FFL dealer in the last 50 years has had a record created. 4473 form, at a minimum, for every sale. Dealer's bound book for inventory, etc. Currently these records are on paper, and are held by the dealers, but they do exist. Dealers who go out of business are required to send their records to the ATF, and they are warehoused. CURRENTLY, the ATF cannot compile those records onto computers, but as I said, all it takes is the govt deciding it needs doing and providing the money to do it with.
Every gun sold that has gone through the "instant check" system, there is a record, of YOU buying a gun. Not a "J. Doe 123 Mainstreet hometown USA bought S&W .38 cal ser# xxxxxx" record (though there ARE state records that do that in some places) but a record that J.Doe bought a gun...
And while there are laws covering what the govt can do with that data, and how long then can keep it, etc., forgive my doubt about the govt always following all their rules, all the time...
We don't have a comprehensive, cohesive nationwide system available to LEOs at the their fingertips, YET, but the basic building blocks are in place, and have been for some time.
Sure, there are millions of old guns that are totally "off the books", and doing house to house searches to find them isn't likely (not even remotely cost effective in so many ways..AT THIS TIME), but they don't need to.