Modified from an earlier answer

The conventional date for the takeoff of the FRG's long-term export success is 1951/52 when the Korean War caused a disruption in international trade that allowed German firms to establish themselves as a major player in international commerce. From the Korean War to reunification, FRG export growth as a whole remained relatively steady, even during global cyclical downturns like the oil shocks of the 1970s.

The postwar success of West German exports did alarm a number of commentators in Western Europe where memories of German occupation and bombing ran long, but there was no equivalent panic or hand-wringing in the United States. FRG products remained somewhat invisible inside the US market for a number of reasons. Firstly, the FRG's primary trading partners tended to be Western European and the North American market remained peripheral to FRG trade. Moreover, FRG manufacturing tended to focus on capital goods like machinery, steel, chemicals, and medium-technology items like precision instruments. Although the FRG did produce high-end consumer products such as Sennheiser's audio equipment, these were often dwarfed by more mundane industrial products. As such, the FRG's penetration of the US market tended to be in items not purchased by an average consumer, such as Krupp-Thyssen elevators and escalators or x-ray machinery.

The one notable exception to this trend was automobiles. Volkswagen had begun significant exports into the US by the mid-1950s and its famous "think-small" campaign helped to cement it as an icon of the 1960s. Similarly, both Mercedes and BMW also penetrated the US market. Yet prior to the 1970s, FRG cars tended to fill in market niches that Detroit either ignored or felt beneath their effort. For example, the VW Beetle was one of the cars of choice for both women and households needing a second car, demographics that Detroit expected to be filled by the used car market. Mercedes and BMW became associated with an alternative luxury market, one which both Detroit and US consumers already associated with European-made products. As such, the wider cultural reaction to these German products on US shores did not resurrect the ghosts of the Second World War since German cars initially were not displacing US manufacturing, but instead serving a need US industry did not attempt to fill. This was in strong contrast to the British reaction to the arrival of the VW Beetle in which tripped off alarms about the ailing British car industry and other forms of industrial malaise. This anti-Axis sentiment would reach US shores in the 1970s, especially with the advent of Japanese compact cars and consumer electronics whose sales outstripped their American counterparts at a time of increased economic uncertainty. Instead, the American reaction to FRG's economic resurgence in the 1950s and 60s was a sort of smug self-vindication that unlike the Soviet-backed GDR, "America's" Germans had learned the valuable lessons of industrial capitalism and were now respectable members of the global economic community- for an example of this mentality- see the Warner Brothers cartoon Word of Mouse in which a German mouse is taught the benefits of mass consumption and production by his more worldly American cousin.

Perhaps ironically, the stigma of the Third Reich upon German manufacturers actually grew as direct memories of the Second World War faded. German industrialists like Alfried Krupp conducted an intensive public relations campaign in the immediate aftermath of the war portraying themselves as reluctant accomplices of the NSDAP who were forced to compromise their private enterprises by a criminal regime. By an large, these efforts were successful and American plans for tribunals against these industrialists fell apart. These early public relations efforts muddied the waters over the actual degree of responsibility of these firms for war crimes and cultivated an image of a German industrialist as a patriotic anticommunist. The American occupation authorities conceived of responsible and strong industry as a firewall against Communist infiltration of the German workforce. Despite notable efforts like William Manchester's The Arms of Krupp, very few commentators in the West took industrial firms to task for their collusion with the Third Reich. The GDR's constant harping about an continuities between the FRG elite and the Third Reich also led to writing off such criticism as repetition of the Eastern blocs' wider talking points of the Cold War. The wider historical reevaluation of Germans' coordination and cooperation with the NSDAP regime in the 1970s and 1980s helped to uncover the broad connections between the state and German industrial firms, many of whom actively competed for allocations of slave labor. Lawsuits against German firms in the 1980s and 1990s by survivors of forced labor helped strip away the vestiges of the postwar whitewashing of these firms' responsibilities. This efforts collectively led to a greater public awareness of the connection of German firms to the Third Reich so much so that it has almost become axiomatic that whenever a German company is caught doing something wrong, such as the VW emissions scandal, there is no shortage of commentary that will mention the unsavory association of these firms with the Third Reich.

Sources

Brady, John, Beverly Crawford, and Sarah Elise Wiliarty. The Postwar Transformation of Germany Democracy, Prosperity, and Nationhood. Ann Arbor: University of Michigan Press, 1999.

Logemann, Jan L. Trams or Tailfins? Public and Private Prosperity in Postwar West Germany and the United States. Chicago: University of Chicago Press, 2013.

Owen Smith, E. The German Economy. London: Routledge, 1994.

Rieger, Bernhard. The People's Car: A Global History of the Volkswagen Beetle. Cambridge, Mass: Harvard University Press, 2013.