That leaves 3 games with "at large" berths available or 6 at large berths. One of those has to go to a G5 team, so that leaves 5 at large berths.

Orange bowl is ACC v. B10/SEC (highest rated non-champion)
Rose is P12 v. B10
Sugar is B12 v. SEC

The Cotton, Peach, and Fiesta bowls do not have set conference tie-ins.

Unfortunately, in 2019, the Peach and Fiesta are semifinal games, and that eliminates 4 of the at large slots. This is an unusual year though. Normally you'll have at least 2 and up to 4 at large slots to fill even after the G5 slot. Even this year when there is only one at-large slot after the G5 slot is allocated, there's an extra slot for BYU if we had a good enough record.

If the season ended today, let's say Clemson, Alabama, Georgia, and Oklahoma get into the playoff. ND would get into the Orange Bowl in the ACC slot vs. LSU. The rose bowl would be Utah vs. OSU. The Sugar bowl would be Texas vs. LSU. That leaves the cotton bowl, who would have to take the G5 team and the choices would be #8 Auburn, #9 Florida, #11 Michigan, or #13 (tied) Wisconsin or Penn State.

If BYU can get into a position where they have a top 10 ranking, then you have a shot at getting picked for the Cotton Bowl. It comes down to who the bowl committee thinks will draw the best among the teams available.

Again, 2019 is the worst possible scenario for an independent BYU. In most other years there are going to be more slots open and available, and a top 10 finish would virtually guarantee a NY6 bowl. In 2019, you'd almost need to be top 8 though.