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.
However, 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 alternative luxury market. 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 was a sort of smug self-vindication that unlike the Soviet-backed GDR, "our" 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.
On a side note, other commentators have been questioning the idea of German "superior engineering," which is a bit absurd. One of the reasons for Germany's postwar export success was that its products were produced with a degree of high standards. One of the things that pops up in American automotive magazines of the 1950s and 60s was that VW produced an automobile that required much less maintenance than American cars. Whether or not German engineering is in actuality more superior is open to debate, but also a bit besides the point. German industry and advertising emphasized the innate Qualität of its products as early as Wilhelmine Germany. During the Wirtschaftswunder years of the 1950s and 60s, FRG advertising consistently stressed that it produced a high-quality product and domestic advertising often disparaged American mass-consumer items as not meeting up to German standards. Although this type of disparagement is true in other advanced industrial states, in the German case, Qualität is often laden with cultural norms particular to Germany. While German superiority is open to debate, it is clear that the perception of superior German engineering has been and continues to be one of the defining characteristics of German manufacturing.
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.