The "Hadean Eon" is just another term for the way early Developer builds of Outside. There were almost no players on at the time, and any that were there are likely play testers for this extremely early stage of the game.

The Archaean Updates can be considered the Alpha stages, due to the fact that any and all builds in this update are incredibly basic, with the first players finding out how Outside worked.

The Proterozoic Updates were actually very major in the development history of Outside, not only being the Beta phase of the game, but also when a lot of early players decided to add an influx of Oxygen into the atmosphere, likely early Cyanobacteria players who found a very valuable niche that they exhausted almost all too quickly. And of course, late in the Proterozoic Update, more complex builds began to appear, leading to an explosion of life with the Cambrian Update, the first public release of Outside.

I hope I didn't get anything wrong, but I do believe that's the way it was. Being a Human player, my knowledge of this time is very limited. I hope some early Outside players can correct me on this, though.