In 1205, the Mongols began their first invasion of the Western Xia, pillaging and burning many outlying villages and cities - this was ordered by Genghis himself and some of the looting was done by Genghis himself.
An alliance with the Jin could be in the works - if it not sabotaged by the coup against Emperor Huanzong either never happened or failed.
(In real world - Huanzong was overthrown by his cousin - an allay of the Mongols and began attacking the Jin once he was enthroned.)
If the coup failed, the Western Xia - Jin alliance in theory could continue.
Yet there is another possibility in the first sentence "In 1205, the Mongols began their first invasion of the Western Xia, pillaging and burning many outlying villages and cities - this was ordered by Genghis himself and some of the looting was done by Genghis himself" - Genghis could in theory be killed in one of these raids setting back the Mongols for decades.