Finland has first socialist Prime minister among EU countries, but only two times left-wing majority in parliament since independence, last time 1968.
Wrong. Poland, Germany and Austria had their first socialist/social democratic head of government in 1918 (Ignacy Daszyński, Friedrich Ebert and Karl Renner respectively).
I assume you were referring to Tanner, who only became PM in 1926. And it's not the first among Scandinavian countries either (see Hjalmar Branting in 1920).
Even friggin Ramsay MacDonald had been earlier than Tanner.