The draft order used by McShay in his mock was based on Football Outsiders' 2018 projections.
McShay called Oliver a "force" and said he was "immensely talented" on the heels of two productive seasons with the Cougars.
In 2017, Oliver registered 73 tackles, 16.5 tackles for loss, 5.5 sacks and two forced fumbles. That came on the heels of a freshman campaign that saw him finish with 65 tackles, 22.0 tackles for loss, 5.0 sacks and two forced fumbles.
If Oliver goes No. 1 overall in the 2019 draft, he will join a small group of defensive tackles who have done so.
Only Russell Maryland, Steve Emtman and Dan Wilkinson have gone No. 1 overall at that position, and it hasn't occurred since 1994.
Teams have seemingly steered clear of defensive tackles with the top pick since Maryland, Emtman and Wilkinson combined for just one Pro Bowl nod between them.
Oliver is a special talent, however, and he would join an already impressive Bills defense that helped lead Buffalo to the playoffs in 2017.
Since the Bills have major question marks at quarterback between AJ McCarron and rookie Josh Allen, a significant regression is possible.
Defensive tackle is an area of relative strength for the Bills with veteran Kyle Williams, free-agent signing Star Lotulelei, 2016 third-round pick Adolphus Washington and 2018 third-round pick Harrison Phillips in the fold.
With Williams likely nearing the end of his career, though, Buffalo could potentially benefit from another top-tier talent at the position.