I agree with W.E.G. - do normal stuff with one exception
The barrel (throat, rifling lands and bore generally) will break in as dozens or hundreds of rounds are put through it. The ONLY difference in your personal field ops when the gun is new, I think, is KEEP THE BORE CLEAN OF FOREIGN MATTER. IMO, the ONLY foreign matter that matters is stuff that has a mechanical hardness sufficient to scratch the gun-metal of the barrel. That would be steel and sand (quartz, silicates, etc. from air dust or the environment). Don't care about powder residue - that's a good lube. Don't care about small-to-moderate copper transfer rub-off (from the jacket of your bullets) - that's another good lube, plus fills voids in the finish of the bore, plus cannot scratch the gun metal, plus can be removed anytime you like.
When first fired, MAYBE steel filings and such could be shaken loose (by the mechanical shock of the round going off) from the reciever/bolt/action area and get entrained into the chamber/bore region by the next cartridge loading in. Maybe. That would be only if the factory did a crappy job of cleaning the parts before assembly or the interior of the receiver area got dirty in shipping or something. Unlikely but possible. Beyond that, the first few firings might break off some burrs or some such from inside the bore itself. Again, unlikely - the bore should have been deburred, at least, if not polished at the factory. But if hard particles from either of these sources lay in the bore when the next round fires, the bullet could drag them along and scratch the bore. Maybe.
So, given these unlikely but possible sources of scratching particles, I would would/will swab or drag a patch from breech to muzzle between each shot for the first few shots (few = more than two, less than 10), to clean the chamber, throat and bore of these particles.