The postwar era witnessed tremendous economic growth, social contentment, and conformity. In the midst of such affluence and comfortable domesticity, social critics expressed growing dissatisfaction with American culture in the 1950s. Explain how the 1950s laid the groundwork for the social and political turbulence of the 1960s.
Part of the answer to your question lies in the question itself. You state the 1950s produced "tremendous economic growth, social contentment, and conformity." While this may have been true for straight white men, it was not true for women or people of color. Schools and neighborhoods were racially segregated and in many places blacks suffered not only racial discrimination but even lynchings and deprivation of such basic rights as the ability to vote. It was only in the 1954 case, Brown v. Board of Education, that the Supreme Court decided that having separate schools for whites and blacks was unconstitutional. Asian-Americans and Hispanics suffered from racism as well, and consensual relationships among gay people were illegal in many states due to "sodomy" laws. Birth control pills were first approved in 1960 but birth control was not fully legalized for all women, irrespective of marital status, until 1972.
What this meant is that many people saw straight white men becoming increasingly affluent but that the so-called prosperity and contentment was only shared by a very limited group of people. Thus the "turbulence" of the 1960s was to a great degree a demand for justice from many of those who did not share in the affluence and were not content with their marginalized roles in society. As more students attended university and media such as television became more widespread, a greater number of people became aware of social injustices and inequality and saw it as a moral imperative to struggle against it.
The 1950s helped to create social and political turbulence by creating a culture of materialism and conformity against which people rebelled in the 1960s.
The 1950s were a time of rising affluence in the United States. The US was the richest country in the world. The middle class, helped by such things as the GI Bill, was increasing in numbers and in wealth. People who had grown up with the stress of the Depression and WWII were buckling down and trying to make secure lives for themselves and their families. They were trying to get material security and they were trying to get psychological security as well by being just like everyone else.
The children of this generation, however, rebelled. They thought their parents were too materialistic and conformist. They thought their parents had no real lives, just these dull existences that were centered around money. Because of this, they rebelled. This was the rebellion that led to the social strife of the '60s. It led to the hippie movement and to the condemnation of things like the Vietnam War and the whole "establishment."
So, the '50s led to the turbulence of the '60s because the conformity and materialism of the '50s made the youth of the '60s want to rebel.