API is a pro level feature. If you go to your game page and click the little settings cog on the top right you'll get a dropdown and one of the options is API scripts. After you click that, on the new page there will be another dropdown for quick install scripts. Choose Group Initiative from the list and save. Next time you open your game you'll have it installed. Check out the wiki for details on how it works: https://wiki.roll20.net/Script:Group_Initiative. Once you have it setup you just create a macro and then it'll work exactly like you want, select some tokens, click macro, and bam everything in the tracker.
Edit: Fixed broken link.