Now having said that; For my hunting rifles,
I have a usually always have hunt purpose and a hunt plan already figured out for it.
As such, I've also got the bullet in mind I want to use.

If possible, I run a quick "experiment" with a factory load that has that bullet.
Shoot two 3 shot groups - Letting the barrel cool between each shot.
I'm looking for first shot fliers and wanting to chrono the velocity and spreads.
This gives me an idea for potential accuracy with my chosen bullet and basic data on velocity.
I'll keep the rest of the box as a standard for life of rifle just in case
I need to go back to these rounds for any future trouble-shooting.
I'll began working-up reloads from this point with my chosen bullet.

Two 3 shot groups from a cool barrel may qualify IYO as "break-in" but really all I do is clean.