If the Golden Horde doesn’t piss Timur off...
Now that I think of it, Timur is responsible for the downfall of at least 2 of the Mongol successor states: the Golden Horde and Ilkhanate, and I wouldn’t be surprised if it turned out that he destroyed the chagatai khanate too, which is ironic as he saw Genghis Khan as his idol.
Without Timur, two or three of the major mongol successor states have a far better chance at staying alive.
The Golden Horde wasn't doing so well before Timur aided Tokhtamysh in reuniting the Golden Horde. It had been suffering internal civil wars for over two decades by 1380, and this weakness had noticeable effects. The Lithuanians took the principality of Kiev, defeating the local beys, and the Battle of Kulikovo was a defeat against Mamai which helped Tokhtamysh in defeating Mamai to reunite the area. Tokhtamysh even burned Mscow in retaliation and forced its capitulation.
Without Timur, Tokhtamysh likely doesn't accomplish these things and the Golden Horde fractures even earlier. That Timur then devastated the Golden Horde later was more a result of Tokhtamysh getting overly ambitious. Prevent Tokhtamysh from acting to provoke that conflict, and the Golden Horde would be in a better position than pre-Timur.
Didn't Timur also make it a point to keep a puppet Ghengisid Khan to maintain legitimacy? They were puppets, but potentially changing the civil wars of the Timurid Empire could result in these puppet khans regaining their power.
You could also have Timur have children descended from Ghengis Khan. I'm pretty sure Timur went out of his way to marry a descendant of Ghenghis, and she remained his most prized wife. They didn't have children however. If they did, these children successfully winning power after Timur dies could arguably leave the Timurid Empire a 'legitimate' successor to the Mongolian Empire.
