your credit card receipts are full of gun, parts, ammo, gunpowder, and other related purchases, and you're an NRA member, and you subscribe to three gun magazines, and belong to a gun club,
The problem with acquiring all that data - billions of records - is that there simply isn't enough time in the day to research the ones at the top of the list. Real crimes go first, then terrorists, etc. If you aren't on the radar, they can't waste the resources to narrow it down and deal with it.
Those billions of records are the problem, not the cure. It's too much information. Take the ATF agent tracking a single gun thru a maze of transactions - especially a pre 68 with no serial number. It has to go thru an FFL to be recorded, and it has to be known from one end of the paper trail or other who did that. The agent has to actually go and look at the record - a musty old journal on the bookshelf in a storeroom, and very likely, not in that state. It only gives him the next step in the chain of custody.
He contacts that purchaser, and gets "I lost it fishing." Ooookay. How did it turn up in a crime two states away? Nope, sold it to some guy, who sold it to some other guy.
There is no record of exactly where every gun is in the United States, and who owns what. In reality, it's easier to just mark the location of gun owners and expect some are there.
When the out of state LEO's went door to door in New Orleans confiscating weapons, ask yourself, are you going to show them all your guns? Do you have them in one container for them to access in one fell swoop? If you really are concerned about the .Gov knowing you have guns, then you don't buy any thru an FFL, and you don't buy any ammo with a credit card, either. You don't buy anything where your face could be recorded. Take it far enough, you start to pop up as someone who's trying to not be seen - which is exactly what the BATF IS looking for, the surreptitious buyer who is avoiding any trace. They watch for that precisely because that is the behavior pattern of those who are handling illegal weapons. It's all hush hush secret squirrel stuff.
Be the grey man. Relish being just another tree in the forest, there's millions of us. It's the ones who manage to pop up in the spotlight who the Feds play whack a mole on. They have their hands full enough with that, Darwin's Law shields us from further scrutiny.
When California passed their assault rifle registration scheme, the results were dismal. They know where those guns are, according to the premise. Did they sweep the state confiscating them? Nope.