Looking through every team's 53-man roster projections on ESPN, it looks like BYU is predicting 10 Cougars to be on opening day rosters this year, with 4 of them in starting roles, and another 3 competing for starting roles.

Predicted Starters are:

Michael Davis (CB, Chargers)
Kyle Van Noy (LB, Patriots)
Fred Warner (LB, 49ers)
Zach Wilson (QB, Jets)

There's also quite a few who ESPN has in competition for a starting role.  While they have them ultimately playing as backups, these could win a starting spot and will see plenty of time regardless. This group includes:

Tayson Hill (QB, Saints - competing with Jameis Winston)
Daniel Sorensen (S, Chiefs - competing with Juan Thornhill)
Sione Takitaki (LB, Browns - competing with Jeremiah Owasu-Koromoah)

Others on projected opening day roster are:

Brady Christensen (OT, Panthers - #4 OT behind Taylor Moton, Cam Erving, Greg Little)
Khyris Tonga (DL, Bears - #3 NT behind Eddie Goldman and Bilal Nichols, in competiton with Mike Pennel for a roster spot)
Jamaal Williams (RB, Lions - #2 RB behind D'Andre Swift)

Predicted to be cut:

Zayne Anderson (S, Chiefs)
Matt Bushman (TE, Raiders)
Zac Dawe (DT, Falcons)
Dayan Ghonwoloku (DB, Rams)
Aleva Hifo (WR, Saints)
Chandon Herring (OL, Titans)
Tristen Hoge (OL, Jets)
Bronson Kaufusi (TE, Packers)
Corbin Kaufusi (OL, 49ers) 
Isaiah Kaufusi (LB, Colts) 
Harvey Langi (LB, Patriots)
Dax Milne (WR, WFT - specifically called out as a late cut)
Kai Nacua (S, 49ers) 
Micah Simon (WR, Panthers)
Chris Wilcox (CB, Bucs - specifically called out as a late cut)
Ty'Son Williams (RB, Ravens)