In part because of leadership -- chiefly thought leadership, a part of which came in the form of assimilation. The power of human capital -- culture -- should not be underestimated. If it's just access to resources like improved food and living conditions, then every group would progress at the same rate. If it's just access to resources, then giving people resources would automatically make them richer. However, there are a number of Africans who advocate stopping aid to Africa. Africa is full or resources, and Japan has very few. Why is Japan so much wealthier?
Most of the answer is human capital.
If the cultures of the Polish and Italians were not encouraging their younger generations to better their fortunes through education and business, then the cultures would have lowered the material wealth of the groups and held them back, in much the same way that the early Irish immigrants to the US lowered the quality of life in their slums.
In this, there is much hope. If cultural transmission can raise up the 19th century potato famine Irish to the 1st world mainstream, there is basically nothing it can't accomplish. (However, culture runs deep, below the level of the conscious mind. It can't be transmitted by simple edict.)
Yes, because of improved living conditions, and better food compared to the old country - not because of political leadership.