According to the map of Gaode, Harbin is 0/027.6 km away from Turkey/KLOC, so you can go there by plane. The fare is about 1500 yuan.
Take the G902 high-speed train from Harbin, get off at Beijing Station after three stops, and then take a taxi to the Embassy of the Republic of Turkey to apply for a visa. After the visa is processed, you can fly to Turkey.