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OP here. I just spent a good bit of my morning searching for this using key phrases like "social mobility without inheritance", "social mobility of the nouveau riche", "sociological studies of wealth accumulation", "wealth accumulation among poor households", etc. in academic and non-academic search engines.
Maybe the only semi-useful thing I've found is this LSE paper looking at 1995 to 2005 (not even published?) about how household net worth is underpinned by housing prices in the UK, something which really shouldn't surprise anyone: https://core.ac.uk/download/pdf/16379905.pdf
>This paper has shown that wealth is very unevenly distributed in Great Britain, with its inequality, measured by the Gini coefficient and using BHPS data, at 0.59 in 2005. Moreover, the analysis has highlighted the widening absolute gap between households with some wealth and those with none or negative wealth. Between 1995 and 2005 financial wealth became even more highly concentrated. Although housing wealth is less unequally distributed than financial wealth and became less concentrated over this period, it continues to be unevenly spread, its Gini coefficient equal to 0.56 in 2005. Over this period, it is particularly the gap between home owners and non-home owners which has increased. While some households in the middle of the wealth distribution increased their share of wealth by becoming home owners over the period, those without housing wealth at the beginning of the period fell further behind.
>[...] Most of the changes in the period were ‘paper gains’ caused by the house price boom. In one sense, this could be taken as meaning that little really has changed: for the most part, owner-occupiers were in the same houses in 2005 and 1995, enjoying the same way of life and the increase in their wealth only happened on paper. However, in the long term the house price boom – unless reversed (which does not look likely at time of writing) – will have effects. First, some of those who own what are now more valuable properties in cash terms will trade down and convert their paper gains into much larger financial assets than they could otherwise have done. Secondly, it means that inheritance flows will be much larger. In that sense, a lot will have changed, particularly for the next generation.
It's still not very informative my original question, as I assume there must also be people that "break through" in terms of financial wealth, as well. But it confirms what the majority of .gs observes in terms of housing and inherited wealth, and it's a place to start.