I know this is an old post, but I will give a +1 to Hero Kids for a few reasons:
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There's like 4 stats and all you need is a bunch of D6.
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The character sheets fit on an index card and are easy enough for a 6 year old to grasp everything on it.
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If you want to run their setting, tons of info is provided with quest seeds and pre-made adventures, and it is super easy to adapt to a different setting, or even totally different genre, because of how simple the stats are.
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It has a great monster compendium, with tons of fantasy monsters, with notes on balancing encounters.
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If you want to get creative and make totally custom monsters, the information included on balancing gives you all the tools to do that.
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The PDF bundle on DriveThruRPG is like $20 for the PDFs of most of the adventures, the core book, the monster compendium, and the gazetteer, all of which are great.
I'm running an ongoing campaign with a 6 year old, a 7.5 year old and my 16 year old sister. We had a 3 hour session last time, and the ADHD 6 year old was there for the whole thing (with a couple 5 minute breaks).
If you have any questions about it let me know. I'm not a super experienced GM. I've only run Hero Kids and Genesys, with being a GM in Hero Kids being my intro to TTRPGs.
I have been playing Genesys, and I LOVE it. I'm not playing in a sci-fi setting, but the whole premise behind Genesys is that is is adaptable to any setting, and from what I have seen of the system, it would be great for something like that. There are tons of rules for vehicle stats, combat, etc. and it has guidelines for how to design and balance your own vehicles.
If you are interested in making and playing in your own setting I would definitely recommend Genesys.
If you are wanting something with an existing setting that matches that vibe, then I'd first check and see if some of the community made settings will fit that, and if not, then maybe look elsewhere.
There are a ton of community made resources for Genesys on DriveThruRPG and also in a dropbox maintained by one of the community members, and that dropbox has some resources for an Expanse setting and other sci-fi stuff that would be a good starting point: https://www.dropbox.com/sh/raqr7usuzwizglm/AACMnwsNyT5DPHyjokWZwQLOa/Community%20Content?dl=0&lst=&subfolder_nav_tracking=1
I would also say you should definitely get the core rulebook AND the expanded players guide, as that has tons of good resources and better guidelines for creating vehicles, as well as other useful things. It's really a fantastic GM toolkit.
EDIT: Also regarding the dice, which can be kind of hard to get, they have an app that you can use, as well as charts for converting normal polyhedral dice to the Genesys symbols, and what I personally do is just use the Star Wars dice, which are the same (with slightly different look to the symbols) and are more available, at least where I am.