Closed Beta for Mario Tour Kart on Android is starting soon! By 22 May 2019, lucky beta testers should have received their beta codes for the game. Note that this beta test is limited to users in Japan and the US.
Those who have been invited would first receive a notification email such as this one, followed by an email with the beta code to the game.
If you want to join other beta tests that may be coming up or stay up to date for news on Mario Kart Tour, you can visit the game’s site.