There is so much BS about first shot out of a cold barrel!
Every rifle I own will clover leave from a cold barrel. Many years ago they didn't though but then I learnt some very basic principles about making and keeping an accurate rifle, so . . .
1 - Lets assume your ammunition is perfect and accurate stuff.
2 - Lets assume the rifle (that includes the crown) and sighting system is in good condition.
3 - The action needs to bed to the stock firmly, exactly and with repeatability - so that generally means bedding it (correctly) unless using a stock with a high grade aluminium bedding block. With a properly bedded action the barrel needs to be free floating as well (this is a modern invention but it works).
4 - A reasonable trigger that breaks evenly, say 2 1/2 to 3 1/2 lbs. That's not some expensive bejazzled match trigger that breaks at half a pound!
5 - Cleaning regime. Don't mother it! Deep clean the entire rifle which includes the bore (decoppering) every 100 rounds or so, maybe less if you want or you feel the accuracy is slipping or maybe more. Once the rifle is accurate you'll know when.
IMPORTANT: Don't leave oil or any cleaning stuff residue in the barrel, wipe it out until clear.
Then all you need to do when you've used the rifle is ensure it is dry, wipe it down and all the parts with a lightly (and I mean lightly) oiled cloth and pull a clean dry (that means not oily!) bore snake carefully through the barrel a couple of times.
Before using the bore snake I occasionally especially when damp clean the chamber with a .410 shotgun mop (again, not oily!).
EDIT: Just occasionally I also use a second .410 mop with a lightly oiled cloth wrapped around the mop first - then the clean dry mop.
I do this every time I've taken a rifle out shooting irrespective of being fired or not (that doesn't mean every time I take a rifle out of the cabinet to drool over it!)
6. Go shooting and you might be surprised! Oh yes, just one other thing . . . when I take the rifle out of the cabinet to go shooting I pull the dry and clean bore snake through it. I don't know why, just habit.