The only way to transfer and be eligible immediately outside of the transfer portal window, is to unenrolled from your current school and enroll in another school, provided you have made no contact with that school’s staff. Because you did not enter the transfer portal, you cannot have any contact with another schools coaching staff until you enroll in that school. They don’t even have to pay their own way once they get there. They can be placed on scholarship. It will be a moot point from now on anyway, since there are no longer walk-ons and scholarship limits, just roster limits.
But once you have participated in a practice, you’re not eligible to play at another school during that season.
If the BYU quarterback had just left school and enrolled somewhere else under the circumstances he did, BYU almost certainly would have pursued a tampering case against them because it’s just not realistic to transfer to a new school and automatically assume that you would be a member of the team. But because he was dismissed from school, it worked out.