How to detect something without using commands and tick.mcfunction

Hi, I'am in a process of making my own "Minecraft minigames" like spleef, parkour etc. and I don't know how to detect that game is started. For example if the game starts I don't know how to get into the first game. I tried to use tick.mcfunction but things like teleporting and giving items are made infinitly and without commands it's really difficult. I also heard about predicates but i don't really know what they can do. Can someone help?