For offline tournaments, you don't need to "start" the tournament. You can begin reporting sets whenever you are ready within the admin. Just go to "Brackets" under the "Reporting" section and click "Edit" by hovering over a set. A modal will appear and you can start reporting results.
For online tournaments, on the same brackets page at the top there will be a button that says "Start Bracket". This will allow players to check-in and start performing their tasks.
Make sure to only start the bracket once round timers are set! For more info on online tournaments please refer to the articles listed here.