If you want to truly even out the playing field, just ban inheritance. You would think this would be a primary goal of pro-equality types but, oddly, even the poorer people in society are against this for various reasons.

We can't ban genetic inheritance, but we compound its effects by allowing wealth inheritance too.

I get that there's sentimentality and people would be against the family home being taken by the state upon death of a parent, but we could give family first dibs on buying the house. The difference being they actually have to buy it, they don't just get it.

But I also think it's important to focus on the thing that really matters which is happiness, not wealth. It seems to me that above a certain level of wealth people can be happy, and that level is way lower than even the median level of wealth in many Western countries. Unhappiness at high levels of wealth comes from the Hedonic treadmill which is driven by inequality. Basically people see others with "more" than them and it makes them unhappy. If they never saw that, they could be happy. So I would study what goods have this effect and massively tax them. Luxury/big cars are a good example.

Any action should not be just to even out wealth for the sake of it, it should be about achieving a happier society (and note I didn't say more productive society etc. that is also something that should only be pursued if it leads to more happiness).