Scholars of Finno-Ugrian linguistics can boast that their field actually predated comparative Indo-European linguistics. János Sajnovics’s work Demostratio idioma Ungarorum et Lapponum idem esse appeared in 1770, fifteen years before Sir William Jones’ rather off-the-cuff and tangential remark on the resemblance between Sanskrit and the European classical languages. Sámuel Gyarmathi (a Kolozsvári, by the way) wrote his Affinitas linguae Hungaricae cum linguis Fennicae originis grammatice demostrata in 1799, some years before any rigorous scientific studies by the likes of Bopp et al. appeared.
Nonetheless, Finno-Ugrian linguistics took a long time to get off the ground, and I think that the problem was simply Finland’s lack of an empire and funds to walk through it collecting all manner of linguistic data. The scholars of fledgling Indo-European linguistics already had grammars of many languages conveniently compiled, and the field moved ahead at a fast clip. Meanwhile, for FU linguistics, it wasn’t until a couple of decades into the 19th century that the first great expeditions were successful organized. I recently bought a delightful history by Mikko Korhonen titled Finno-Ugrian Language Studies in Finland 1828–1918 (Finnish Society of Sciences, 1986). It reveals that it was actually an Indo-Europeanist, the eminent Rasmus Rask, who helped get things off the ground:
One crucial factor was Rask’s visit to Finland in 1818. Rask only remained in Finland for about three weeks, but during this short stay he had time to meet, among other, [Gustav] Renvall who taught him Finnish daily, and [Reinhold von] Becker. There has already been talk of Rask helping to get Renvall’s dictionary project off the ground. It is quite obvious that Rask’s influence, as a pioneer of comparative linguistics, on Finnish scholars in Turku was, in any case, inspiring and productive. Rask’s most important achievement was his contribution to the idea that had been under discussion since Porthan’s time, about the possibility of an expedition to the Finnic peoples living in Russia.
In 1816 Count N. P. Rumyantsev had asked bishop Jacob Tengström (1755–1832) to nominate two Finns who would be willing and qualified for an expedition that was to form part of Rumyantsev’s extensive research projects in eastern Russia. Tengström recommended Renvall who had already shown his skills as a scholar of Finnish, and E.G. Ehrström (1791–1835) who was a scholar of Russian language and history. However, other commitments on both sides meant that eventually the plans for the expedition were canceled. The expedition was still discussed in both Turku and St. Petersburg and several names were put forward. In 1819 a young Finn, Anders Johan Sjögren, informed Rask in a letter passed on by Renvall that he was willing to make a study of the Finnic peoples living in Russia. Rask was, at the time, living in St. Petersburg and was in contact with Rumyantsev. Sjögren was invited to come to St. Petersburg so that he could make himself known and demonstrate his skills for such an expedition. Sjögren travelled to St. Petersburg the following year and made his first expedition in 1823. Finally, in 1824 he set out on his long journey among the Finnic peoples that was to last five years. Thus began a career that was not only important in terms of Sjögren’s own accomplishments, but also because it laid the foundations for later research, for example, the work of M. A. Castrén.