With respect, there was no international element to the genesis of this war, whatsoever.

As for "the most powerful nation I the world, backed up by its regional allies ...", what a laugh.

With allies such as AK, Saudi Arabia, and Likud, who needs enemies?

The war in Syria, like the 30 Years War, started out as entirely internal matter.

But after the elimination of the democracy-desiring rebels as a serious force, it became a regional struggle, with local proxies, where, ultimately, there cannot be peace in Syria without foreign struggles being resolved.  For Hapsburg and Bourbon, read Saudi Arabia, and Iran.

Where once Austria, Spain, France and Sweden fought over the carcass of Germany laid waste, ...

... today Saudi Arabia, Turkey, Russia, and Iran fight over the carcass of Syria.

America (and NATO) are essentially irrelevant to this fight.  They are bystanders left to save Jordan and deal with a refugee catastrophe.