https://www.fangraphs.com/depthcharts.aspx?position=ALL&teamid=14
We need to beat the 2nd wildcard's projection in WAR, approximately. Let's set that baseline at 40 WAR, the team currently projects at 29.6 as a team, with the Angels and A's the top two AL Wildcard teams in the 37-39 range.
Assuming no one underperforms, and looking at guys who could somewhat reasonably beat their projections to give us 10 more WAR, we'd need:
- Stroman provides 4 WAR (career year), Aaron Sanchez 3 -> +3 team WAR
- Matt Shoemaker and Ryan Borucki with 2 WAR each -> ~+2 team WAR
- the bullpen as a whole provides 4 WAR -> +2 team WAR
- Grichuk becomes a 3-3.5 WAR player, his backup is at least replacement level or just above -> +1 team WAR
- LF: McKinney + Teoscar platoon provide 2 WAR -> +1 team WAR
- SS: Freddy Galvis plays to his projection and Lourdes Gurriel adds 1 win here -> +0.5 team WAR
- 2B: Devon Travis gets knee replacement surgery, Brandon Drury isn't awful, Gurriel adds 1 win here -> +1 team WAR
- C: Danny Jansen really is that good, 3 WAR player -> +1 team WAR
If all or most of that happens to a reasonable level - say Sanchez is "only" a 2 win pitcher but Bo comes up mid-season and Gurriel plays FT at 2nd - then that's a second wildcard team. This assumes Vlad Jr.'s nuts projection is accurate, which doesn't factor in him being a potentially awful baserunner and/or defender, Pillar doesn't decline, and the bench and fifth starter logjam doesn't completely s*** the bed. Also the A's don't Moneyball their way to another big year and the Angels don't overperform the projections.