Keep in mind I've only read the rules, not actually played the game yet.
I love the theme and execution of this game. I feel the incredible time spans you are working with are a bold choice that make this game really stand out, and while the end is (possibly, probably) bleak, it feels downright optimistic that the game portrays humanity having such a long future ahead of us.
Your rules are clearly worded and I like that the structure of the rules document really guides the reader through it. Clearly stating goals of the game and going through the basic structure of the game up front are a big help.
I also love how much mileage it feels like you're getting out of the deck of cards, as a resource, pacing mechanism and story/character prompt. Really good use of limited playing materials, that.
My one concern was going to be that it might be hard to figure out exactly how to frame the scene and play out the challenges, but the included example challenges in the legacy of humanity sheet probably helps a lot with that.
Impressive work, thanks for sharing!