I ran into this today. I think the cause is if you have the options menu open during the pick screen when the game starts. After the game starts, the mouse stops working (other than being able to scroll the map by moving the mouse to the edges of the screen). Both right and left click do nothing including on the minimap, buildings, units, etc. Alt-tab doesn't fix it (I alt-tabbed and back into the game several times). It appeared to get fixed after I pressed escape.
The reason I had the options menu open during the pick screen is actually because the music is way too loud on the pick screen. I have the music set to 10%, and it is still absolutely overpowering. I'm not sure if this is just the music setting not being respected on the pick screen, or if it is just that loud. Turning down sound globally on my computer is not an option because I'm comparing the volume of the music to the volume in discord, and the music is much louder than people on discord even when the setting is at 10%. When in-game I don't have this issue.