The obvious answer is that it's only possible if Hughes wins in 1916. But there is perhaps
one way Cox can win in 1920 even if Wilson wins in 1916:
The POD is a healthier TR who is alive in 1920--and once again denied the GOP presidential nomination by the Old Guard. Angered, he once again runs a third-party campaign, allowing Cox to win with something like the 34.1 percent of the popular vote he got in OTL...
https://en.wikipedia.org/wiki/1920_United_States_presidential_election
This is very unlikely, I know, but it's the only even-slightly-plausible way to get Wilson in 1916 and Cox in 1920 I can think of.