On newly chambered barrels I fire one round and clean and lube it. I do this each time for 10 rounds. Then I fire 25 rounds cleaning it after every 5 rounds. This will ensure that no burrs are left in the chamber or in the barrel that can cause copper to build up on imperfections.
Pretty close to what I do.
Usually, VERY good cleaning before you shoot it.
Remember, some barrels/top ends are test fired at the factory and have fouling from that, or from chorming process or shipping anti-corrosion residue (or all of the above).
Also, there are usually some pretty jagged burrs are left dangling from the rifling after the manufacturing process, and a very rough/through initial cleaning will remove the worst of these so they don't imbed in the barrel somewhere...
Once you have it clean,
Take it out and fire ONE round, then clean, fire another round until you get a CLEAN patch out, then fire again, ect.
Do that for 10 or 20 rounds until you get to where 2 or 3 patches will clean it out quickly.
Then fire Two or Three rounds, clean (and it shouldn't take more than 3 to 5 patches to clean) for about the next 20 to 30 rounds...
The idea is, copper is 'Liquid' or a 'Hydraulic' force at the pressures we are talking about when the rifle if fired.
Copper will invade EVERY scratch, void, pit, tool chatter mark, overhang on the rifling, ect. if you don't clean between rounds, those defects, burrs, ect. will be full of coper and NEVER go away.
Copper can collect in the voids, and actually move the metal in the barrel aside (under hydraulic pressure forming conditions) and cause all those defects to become LARGER, and that will ruin longevity and accuracy, and in extreme cases, actually make the barrel unsafe to use.
It's not as big an issue in heavy, hard chrome lined barrels as it is in untreated steel, but it will still effect accuracy and longevity of the barrel.
If you clean the copper out between rounds when breaking in a barrel,
Then the metal will lap over it's self, taking on kind of a 'Fish Scale' appearance in pits and shallow chatter marks/scratches,
And on Deep defects, the edges of the scratches/ect. will round over with wear, where it doesn't shave jacket off the bullet as much.
Hard Chroming usually takes many of the defects from machining out of the barrel...
But you still need to break in the barrel and 'Slick' it down before putting it into hard service.
It will be MUCH easier to clean, last MUCH longer (if kept clean) and make the rifle more accurate to boot!