There are many ways to obtain a gun in America, with varying levels of records of it being recorded:
1. Buy or transfer a gun through an FFL, in which case a Form 4473 is filled out and kept by the FFL. The ATF, in the course of an investigation can get a copy of this form to see who bought the gun. The ATF cannot legally go around making copies of all 4473s to create a database. The information from the 4473 is required to be kept on file with the FFL for at least 20 years, at which point he can start purging it. If he quits being an FFL before then, he turns it all over to the ATF to keep the records for future investigations. So a few guns that are sold through an FFL will eventually have no record, if he holds the FFL for 20 years after the sale AND decides to destroy the record.
2. Buy a gun in a private sale, assuming your state doesn't require this to go through an FFL (in which case, see #1). Most states require no record keeping for this. Where I live, my only responsibility under the law is to be reasonably sure that the buyer is not prohibited from owning guns. That means I ask, "Are you prohibited?" and if they say no, I can sell it to them with no liability.
3. Receive a gun as a gift. Most places treat this the same as #2.
4. Make your own gun. Most states don't require you to register a gun you made yourself. You must be making it yourself, for yourself. If you later decide you don't want it, you're supposed to transfer it to its new owner via an FFL. Making a gun yourself is much easier than it sounds; I've built an AR15 for myself, it has no serial number on it, there's no 4473 for it anywhere, and it's 100% legal.
So, methods 2,3 and 4 can create new gun owners with no record of it, and method 4 can create new guns with no record of it.
Method 1 can make new owners with no record assuming certain rare events: FFL in business long enough to start purging his books, or his store goes up in a fire and the records are destroyed, or thieves steal the records. In this case the ATF can only learn that a gun existed at some point; they have no idea who the original retail owner was, so their information that it existed is useless.
With home made guns, they don't even have that information.
So, NOT every gun in the US has paperwork for it somewhere, and NOT every gun buyer is on paperwork somewhere, and what paperwork does exist for some guns is 100% useless with regard to locating the gun or its owner.
This whole discussion doesn't even touch on the subject of a more important question: What good do records and serialization do when most guns used in crimes are stolen to start with? Despite what you learned by watching CSI, the answer is a resounding, "Not a whole hell of a lot."