Some early research in Oregon claimed that voting by mail increased turnout by 10 percentage points. However, since then, scholars have been unable to reproduce those results. Apparently that boost to Oregon’s turnout grew from a “novelty effect” and recurred only in special elections.
In Washington, researchers found that switching to all-mail elections increased overall participation by about three percentage points in presidential and midterm elections
https://www.washingtonpost.com/news/monkey-cage/wp/2015/12/21/voting-only-by-mail-can-decrease-or-increase-turnout-wait-what/

From 2000 to 2014, Oregon averaged a 44% return rate in primary elections.  Not exactly the silver bullet.