Alright here goes:

So at the end of WWII you have this influx of veterans returning to the US.

This posed a social problem that, in a post-WWI country, was often disastrous. The early proto-fascist and pro-fascist paramilitaries that wracked the Weimar Republic and helped bring the Nazis to power and to intimidate/suppress the opponents of the Nazis (along with terrorizing German Jews etc.) were made up by a majority of returned WWI veterans who were pretty fucked by the war and often struggled to find work and reintegrate into a post-war society, although they knew how to conduct war and they were roaming the streets, so it created a powderkeg of malcontents. These WWI veterans across Europe caused a great deal of political strife throughout the interwar period.

I haven't read any sources where the US government was specifically aware of the political problems posed by veterans from WWI failing to find work and to reintegrate into society, thus causing political strife, but it'd be hard to imagine that they weren't aware of this and that thus that their policies towards WWII veterans weren't influenced by trying to pacify and neutralise this potential political problem.

So WWII veterans return to the US and the US creates the GI Bill which was a massive welfare program designed to bolster the US economy domestically while also providing for the needs of the WWII veterans.

A large part of the bill was aimed at providing low-interest rate, no down payment home loans to veterans and the funding preferenced new builds.

This created a massive subsidy for the construction industry and it was the Levitt brothers who used this influx of funding to create low cost, mass produced housing outside of the city areas, the most famous of which was Levittown town (humble folks, those Levitt brothers eh?)

This was essentially the advent of suburbia.

Because of the low cost that housing loans were provided at, it was actually cheaper for veterans to buy new houses in the suburbs that were springing up than it was to live in the city.

Although, this is post-war America we're talking about so obviously this is when Jim Crow laws were still gripping the country and, of course, the GI Bill catered to the political interests of those who supported Jim Crow.

Effectively, what this meant was that the GI Bill massively preferenced white veterans and it actively and passively discouraged non-white veterans from benefitting from the bill.

As one example of this, in the New York and northern New Jersey suburbs 67,000 mortgages were insured by the G.I. Bill, but fewer than 100 were taken out by non-whites.

So, basically this was economic apartheid.

Not only do we have the creation of the suburbs and all the car-dependence that comes with it happening right there, we also see the emergence of the so-called "middle class" which was overwhelmingly white in its makeup because this housing freed up disposable income and it fostered intergenerational wealth from the investment into property that suburbia allowed for.

Although people of colour languished behind and were excluded from property ownership through the design of this bill and redlining, so they tended to stay stuck in inner city slums which cost a lot more for housing than a cheapz subsidised home loan in the suburbs offered.

Over time there was a strong push to "clean up" the inner city and to eradicate slums. You see these massive housing projects developing from the 1930s as cities became gentrified, and perhaps the most famous example of public housing projects is the much-maligned Pruitt-Igoe project (which has a fantastic documentary on it called The Pruitt-Igoe Myth.)

These projects concentrated poverty and "criminality" (if you'll excuse the shitty term for the sake of my vain attempt at brevity here) due to complex issues of economic and social exclusion, intergenerational trauma, drug/alcohol abuse etc. and they also were extremely exploitative. Some residents of Pruitt-Igoe were spending up to 3/4s of their income exclusively on housing, which perpetuated the cycle of poverty for black Americans.

So you have this dual effect of the middle class emerging and creating generational opportunity and wealth in the nascent (white) middle class while people of colour are excluded, stuck in expensive slums, and then they are shifted out of the slums and into public housing which was arguably worse than the slums in many ways as it disrupted the established communities and displaced local businesses in order for property speculators (especially slumlords) and property developers to cash in on the gentrification of the inner city.