Yes, 67 years ago in 1952. Anyone can live there now if they have the money. Unfortunately, the problem in Levittown, like the problem with the rest of Long Island (and many other areas of the country) are that housing prices are massively inflated and taxes are insanely out of proportion of the services you get back for paying them.
For the honor of living in an average small house in this economically depressed area you can look forward to shelling out ~$500,000 and paying $8,000+ a year in property taxes. That's the real obstacle for working people to come move to places like Levittown. A few decades ago young, working people looking to start a family could buy a house in a place like Levittown for 2-3x their annual income. Now its more like 8-10x of their annual income. It isn't economically sustainable, like much of the rest of our economic system, and it has absolutely nothing to do with racism.