Three weeks ago, it was announced that college football playoff would expand to 12 teams starting in 2026. The format is as outlined by ESPN:
The four highest-ranked conference champions will be seeded one through four with each receiving a first-round bye. Teams seeded five through 12 will play each other in the first round on either the second or third weekend of December. The quarterfinals and semifinals will be played in bowl games on a rotating basis, and the championship game will be at a neutral site, as under the current four-team format.
To clarify, this means that Notre Dame - or any other independent - will never have the chance at a first-round bye, because they will never play in a conference championship game.