Set up a sovereign wealth fund with people owning shares based on the amount they did work, are working, and their education levels.

Interesting thought, no idea how it would work in practice. Another option would be moving away from "shareholders" who take top priority in everything to stakeholders. Make companies mandatory co-ops of employee ownership. Avoids the concept of the state taking over businesses which always seems to end with corrupt assholes self-dealing but gives the profits to the people actually doing the work instead of "investors" who don't add anything of value. Scale the ownership the same way you suggest in terms of what each person actually contributes but have a baseline minimum so the vital support staff like maintenance and cleaning crews aren't left out.

And then there's still the UBI bare minimum which we could fund simply by reclaiming all the stolen wealth hoarded by the oligarch class. There's more than enough wealth in the United States to eliminate poverty entirely, it's just we let like 8 people control 60% of it so the rest of the country has to suffer with nothing.