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. A side bar in Melvin J Lasky's rather fawning 2 October 1955 NYT's article" The Volkswagen: A success story," captured this complacent mentality. After noting to its readers that although the Beetle was the fastest-selling foreign car in the US, the sidebar contended:

But despite the popularity of this small German car, there is little likelihood, in the opinion of the automotive industry, that Detroit will soon follow suit. The manufacturers are convinced that the demand is not big enough for small cars. They point out that a year-old car- fully equipped - is cheaper than a new Volkswagen, and they add that it costs almost as much to tool up to build a small car as it does for a large one. In the event of public demand, however, the industry is prepared to update plans it had long shelved for small cars.

Similarly, a 10 April 1957 Wall Street Journal article on European economy cars quoted both Harlow Curtice of GM and L. L. Colbert of Chrysler somewhat curt dismissal of these smaller automobiles, with GM's executive noting they were uniformly "substandard" and Colbert noting Chrysler had designs for small cars dating from before the war, but had no plans to start production of them.

This somewhat complacent attitude to this West German product 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. Advertisers for British cars like the Sunbeam Imp and MG 1100 explicitly tried undercut Beetle sales both domestically and abroad by comparing themselves favorably to the German product. The Imp was specifically priced $100 below the Beetle. Pressure from British manufacturers led higher tariffs on imports in 1965, to which VW responded by imposing a ban on British parts. French car maker Renault likewise saw Volkswagen as its major competitor and its advertisements both at home and abroad stressed the superiority of French cars to German ones.

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. Lasky called VW's Wolfsburg Dearborn-on-the-Luneburger-Heide and noted the city "is 'American' only in the sense that it too is a great melting pot, with a rootless population to find opportunity and pursue happiness." Lasky also drew a picture of its chief Heinrich Nordhoff that likened him to a figure that melded old-world charm and the savvy practical modernism American businessman. Vinton McVicker's 20 Mar 1956Wall Street Journal article "People's Car: Defying Detroit Dogma, Volkswagen Triumphs In Global Markets" favorably compared both VW and Nordhoff to Henry Ford. A 10 October 1962 Wall Street Journal piece on Nordhoff explicitly stated:

Dr. Nordhoff wasn't a Nazi. He was and is a patriotic German. The Hitler government needed experts, and Dr. Nordhoff qualified. By 1942, he was director general of the Opel-werke in Brandenburg, then the largest truck factory in Europe.

The NYT's 1968 obituary for Nordhoff also took pains to point out he had never joined the NSDAP and treated his initial blacklisting by the occupation governments as an unfortunate interlude in a career of West German industrial development. Although both the firm and its chief's Third Reich past was an open secret, at one point in the war, forced laborers made up half of the Opel-werke in Brandenburg's labor force, the American press preferred to tell of a more edifying story of West Germany prospering under American tutelage.

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.