Green Stars had their debut in Super Mario Galaxy, but they didn't play nearly as big as a role in that game as they did in the Sequel to Galaxy, and the eventual successor, Super Mario 3D World. SM3DW took a different approach as a Star Coin replacement, but Galaxy 2 used it as post-game content to extend the story some more, which results in being able to double your star count compared to the previous 120 stars that were required to unlock the Green Stars.
However, a hacker that goes by the name of "Arthurtilly" took to hacking the entirety of Super Mario 64 to include these Cosmic Gems. Right off the bat, you'll realize that you can enter any stage in any order, with later stages having harder difficulty stars to collect. If you think you can just go defeat Bowser immediately, then you'll realize that the pipe to the final fight is blocked with a Star Limit. You must collect all previous 120 stars to access the fight, plus a fully-custom bonus level.
If you would like to play this hack, you can follow this link, or just simply search "Super Mario 64: The Green Comet" to be led to a release trailer.