Your challenge is to create a country that greatly surpasses that by having a society that is almost entirely geared towards science and technology.
Ok, I know this isn't the most likely idea ever (mine rarely are), but have a little imagination!
In my view there are three ways this could possibly come to fruition:
Privately sponsored colonization: Some rich philanthrope decides that the best way for him to serve humanity is to create a science colony in some uninhabitted or underpopulated part of the globe. He sets up a universities and research centres there and manages to get a large number of scientists and engineers to move. With time, the place pretty much becomes nerd heaven and so all the scientific geniuses in the world want to move there.
Forced ressetlement of scientists. The idea is to have some crazy dictatorship, say Stalin's Soviet Union or Nazi Germany, put all their scientists in one place so they can control better and have them develop all kinds of expensive toys for militairy and showing-off purposes. Then, when the regime falled, the place would somehow manages to gain independence.
An already existing small nation finds reasons to invest more and more in science and gradually develops this kind of society.
If you think you need to, I guess you could place the PoD somewhen in the 19th century, but I decided to put the thread in this subforum because the 20th century was the one with the most significant scientific and technological advances, and there should certainly be a way to do this with a post 1900 PoD. As I said, use your imaginations!