Were there international Islamist movements before the US started supporting islamists during the USSR's war in Afghanistan?
Especially if international means movements across what would later become national or colonial boundaries. A lot of modern Arabic and eventually resurgent Islamic consciousness arose from the collapse of the Ottoman Empire. The success of revolutionaries, like Hussein bin Ali* to frame pan-Arabic nationalism as an Islamic revitalisation versus the mostly secular bureaucracy of the late-stage Ottoman Empire, allowed for aspiration towards new Islamic Golden Age. The contraction of the British and French Empires a few decades later had a similar effect on regional sentiment.
The Cold War simply brought home that neither the USA nor USSR were honest brokers for Muslim interests. Islam was always an international movement; the USA managed to selectively breed militancy into the international milieu by funding and training specifically those Muslims willing to kill for their religion.
Because fundamentalist Islam is a repellent doctrine (like all religious fundamentalism); the mainstream Western narrative tends to forget that the modern Islamist movement is also quintessentially an anti-imperialist movement. The "international Islamist movements" have existed as long as European interests in the Middle East have.
* Of Lawerence of Arabia fame.
I'm assuming you're referring to the use of terror by international Islamic groups post-WWII.
First I would note that terrorism is a very vague term (by my definition more or less every armed group involved in conflict has used fear for political goals).
That being said the US was helping Afghan militants in the 80s. There were dozens of "Islamic" groups of varying degrees of religious observance before that.
Algerians fighting their war of independence against France in the 50s-60s were labeled terrorists and small attacks were conducted in France. Several Palestinian and Lebanese militias were active after the establishment of Israel. Several high profile airline hijackings in the 60s-70s done by these groups.
It should be noted though that Islamism "a la" Al-Quaida is a relatively modern concept. Most of the groups active between the 60s-80s were primarily influenced by nationalism.
One of the reasons for this rise may be the end of the Cold War. A lot of anti-Western groups were sponsored and/or trained by the Soviet Union, and as such had some "communism" rubbing off on them. The PFLP was a Marxist/Communist Palestinian group that at one point was the most popular Palestinian militant group. After the end of the cold war they slowly faded and gave way to Islamic Hamas.