Germany invented the modern research university, which let them become world-leaders in much scientific research in the late 19th century (if Nobel Prizes had been awarded in the 19th century, there would have been many German winners). The prototype of the research university was Universität zu Berlin, officially opened in 1810 (but teaching had started already in 1809), which is today Humboldt-Universität zu Berlin.

The new style of university was very successful at producing good research and good researchers, and German became the must-know language in science (replacing French, which had earlier replaced Latin), and German scientific journals became the must-read journals (those "must"s are tempered by the translation and publication of German papers in scientific journals published in other countries, but the translated papers were only a small fraction of the total German output).

In summary, Germany did it by developing an effective system for research and research training, and putting sufficient funding into that system. Once German success was clearly visible, some other countries moved to do the same kind of thing. In particular, the USA was a fairly early and successful adopter of the new type of university, with the first research PhDs in the USA were awarded by Yale in 1861, with Johns Hopkins soon following as the first established-as-a-research-university university in the US in 1876. In comparison, the UK awarded its first research PhD in 1920, and Australia in 1949.

The USA was growing as a real rival to German research dominance near the end of the 19th century. German research had essentially peaked, while US research was still growing - the US would take Germany's place as the world leader in research eventually, and English would replace German as the essential scientific language. Events in the early 20th century made this happen sooner than it need have done. WWI disrupted non-military research in Europe - this included German research. The war badly damaged the German economy, and the Great Depression which followed did even more damage. Already in the 1920s, the decline of German science (or at least German physics) is visible in the German language journals. Unfortunately for German science and German scientists (especially German Jewish scientists), the Nazis took over the government of Germany and did even more damage to what had been the world's greatest research system. Many of the best German scientists left Germany, and carried out research and trained research students in their new countries (Max Born being notably successful in training students who would go on to win Nobel Prizes, in addition to winning one of his own). Thus, the Nazis simultaneously badly hurt German science and helped science and research in other countries.

There were still skilled German scientists and engineers, who still carried out good research. However, the were fewer than before the Nazis, and less well funded than they had been before WWI, and German world leadership in scientific research was gone.

This answer was partly based on my earlier answer in https://www.reddit.com/r/AskHistorians/comments/dv4ppq/when_was_the_first_phd_awarded_and_what_led_to/ which includes some references that might be of interest.