There are a great many caveats to this, but for now we have some official dates for the start of the 2021 minor-league season: Tuesday, April 4* for Triple-A, and Tuesday, May 4 for Double-A/A. The season will go through the penultimate week of September, for 142 total games for Triple-A clubs and 120 for Double-A/A. (The staggered opening dates for the different leagues is due to lower-level minor leaguers arriving at Spring Training only after members of the big-league club have departed at the end of March.)
*The Tacoma Rainiers will play their first game as part of Triple-A West-West (groan) April 8.