Are there any time lines where Genghis Khan doesn't exist, doesn't unite the Mongols, or gets killed invading the Jurchens leading to the collapse of the Mongol Confederation? How about good discussion threads? This is something I'm interested in writing about myself, but I don't know how often (and well) it's done.
Feel free to use this space to talk about the POD, of course.
The butterflies from this are so enormous that one could invent almost any narrative off it.
To explore it seriously...
One would have to start with Chinese politics in the 1200s - the internal state and probable development of the Jin Empire in north China, the Later Song in south China, and their relations with the satellite states of Hsia Hsia and Nan Chao.
China had been divided into two states for roughly 100 years. AFAIK this was an equilibrium; if it continued for another 100 years, it might have become permanent.
This also links to the economy of the western Pacific; AIUI, the later Song was a great mercantile state with connections throughout that region. How much were these connections disrupted by the Mongol conquest?
In another direction, one would have to explore the politics of central Asia - in particular the Sultanate of Khwarezm. Also of south Asia - the Sultans of Delhi repelled several Mongol attacks, but those attacks had effects and consequences.
Next look at the conditions of Russia - in particular Kiev, the dominant state in pre-Mongol Russia. Also Persia and Mesopotamia - and the sack of Baghdad had effects on Islam which echo to this day. (I heard an Imam preach a sermon on the sack of Baghdad only a few years ago.)
The Mongol invasion of Seljuk Turkey affected the Byzantine Empire's successors.
Thus a real no-Temujin TL would require a detailed knowledge of 13th century history in China, the western Pacific, central Asia, India, the Middle East, and eastern Europe - just to get through the first 50 years or so.