The bullet is either stable or unstable. If the latter, there is no doubt. Some bullets will print sideways.
When a bullet exits the muzzle, it wig wags a bit. It takes awhile to spin true. This has no effect on accuracy, and it takes a close eye and quality paper stock to discern the slight wig wag. In the early 20's Mann ran tests with the bullets passing through a series of targets, and he was able to measure the wig and the wag. It was usually gone by 50 and always gone by 100.
The Bullet's Flight From Powder To Target: The Internal And External Ballistics Of Small Arms (1909) A good read.
The wig wag means nothing in the real world, except for testing bullets. If you want to see how a bullet performs, say by shooting it into wet phone books (do they still make those?) you should shoot them at 100 yards. The velocity will be more like what you hit a target at in the filed, and most important, you want the bullet not to hit slightly sideways, as it would at 25 yards. This tends to blow bullets up or prevent proper expansion.
Stability (spin rate) must be adequate at the muzzle, other wise the bullet will tumble. And once it tumbles, it will never recover. If it is stable at 10 yards, it will always be stable, because it gains stability as it goes down range. As it slows down there is less air compression, so the less dense air requires less RPM to be stable. Since the RPM does not slow nearly as quickly as the velocity, the bullet gains stability.
Mann knew all this in 1905.