Well, what has always worked for me with a brand-new rifle is to get the scope mounted and bore-sighted and then shoot one round at a time at 25 yards and adjust the scope as necessary. It usually takes maybe three shots to get it to dead center. Sometimes four, with appropriate griping.
That gets me on the paper at 100 yards, not far off the center, and I do three-shot groups and get the group center to two inches high. Commonly takes maybe three groups. Then I'll shoot a five-shot group to check just how the rifle does. By the time I've done all this happiness, I've usually run fifteen to twenty rounds through the rifle.
If I feel I need to tweak the rifle a bit to get better groups, I'll do stuff like clearance the forearm and then shim, or maybe work up a different load. Then, back to testing.
That's always worked out to Bambi's detriment.