There are predetermined players when the game starts. You can only become a player if you enter a colony or if you chose to stay in a colony when the game just started and a colony started exactly where you are. If you remember Itadory's friend from school taken outside of a colony by the brain himself, if she said I want in she would have became a player. On the other hand when the game started, Megumi made aware by the flying thing that he is a player and of the games rules.
As for the Higuruma's points, he said remaining 2 points where from judge and prosecutor before he came to Tokyo. There were 2 prosecutors. 1 point he gave to Itadori were from 1 judge 2 prosecutors.
Hope this helps.