'til it starts throwing rounds or loses accuracy. You haven't allowed it to reach equilibrium, so that might be 100+,... Don't even boresnake it unless you've inadvertently dropped the muzzle in the dirt, or had dirty ammo, etc. in the chamber/barrel. If you must clean it, use a good CARBON cleaner with a nylon brush, not something that is going to take out the COPPER and see how it shoots after a few fouling rounds - in my experience, it will return to what it was doing for another 100+ rounds. Reserve the use of a copper cleaner for when you aren't returning to accuracy after using the carbon cleaner - this could be several hundred rounds(!) At which point, you'll clean it with a copper cleaner and have to put about 20 rounds down the tube to reach the copper equilibrium I'm talking about and it'll start shooting bugholes again. Unless you're using really old surplus ammo, todays powders are not corrosive and copper is your friend, so don't worry about your barrel,... let it be. I know it seems counter-intuitive, but cleaning is often overdone and hurts accuracy,... especially the use of copper cleaners.
From your last post, I can surmise that you don't reload and are restricted to use what you can find at an ammo supplier. In that case, try some different ammo once you've sent a bunch of the stuff it doesn't seem to like down the tube i.e. reaching copper equilibrium in the barrel. While Fed Gold is certainly a good brand of ammo, and they try to keep the tolerances tight from batch to batch, it doesn't mean your rifle will like the batch you purchased. Guys who shoot .22LR competitively will try all kinds of different ammo and batches of ammo in an effort to find the ONE batch their rifle likes as they can't reload the rimfire cases,... Only THEN will they buy a truck-load of it.
If you're ever going to start reloading, the .308-Win is the perfect starter caliber - tons of components, and time-tested recipes to utilize. Again, 175-SMK's over 43.0gr of Varget is a great start. Pick up one of the many reloading kits available from a reputable manufacturer (Redding, Hornady, RCBS, Lee,...etc.), a set of good dies, some bullets, primers, and powder and go for it,... You'll REALLY see how accurate it can be as you can now tune the load to your rifle.
Ry