In over a half a century of OCing....I've never had a firearm checked to see if it's stolen or had to prove it's mine.
Welcome to OCDO.
When I was enjoying my colliloquy with the Surry County Sheriff's Seargent he kept demanding I produce my gun's "papers". I still am not aware of any organization except S&W that can provide a pedigree, and since all my handguns are housebroken I did not have piddle pads to hand over.
If a cop wants to claim your handgun (or car, or pocket comb) is stolen property he fills tells you he is placing you under arrest then goes to a magistrate where he fills out an affidavit about why he thinks the item in question is stolen. If the magistrate believes the stoty being told a warrant is issued and the rodeo begins.
It takes time and money to sue the cop for defamation of character, false arrest, and walking upright while impersonating a human being. You may or may not win.
It takes "guts" to tell the cop to go ahead and arrest you. Some folks do not want to deal with the time and inconvenience needed to fight and may consent to some sort of agreement to have the charges dropped in exchange for having the firearm confiscated.
But the real point - and question - is "Why are you expecting some cop to acuse you of having a stolen firearm in youor possession?" There are all sorts of other charges they can use to yank your chain - and those charges do not expose them to the liability a false accusation of possession of stolen property might.
New owners/carriers are all Nervous Nellies. Heck, I bet you were nervous when you started riding a bike or driving a car or going out on your first non-double date. You get less paranoid and more confident as you get more experience.
Come out to OC events (lunch/dinner) in NOVA and meet folks with a bit more experience than you currently have. Ask someone to accompany you on an OC walk - even if it's just from the parking lot to some eatery and back to the car.
I'll share the best advice I ever received. "Breathe. Breathe in, then breathe out."
stay safe.