George Washington made a contribution to getting that war going, but I'd say that the war was in any case inevitable. The French and British empires had conflicting interests in North America (as well as elsewhere), and would certainly have gotten into that war regardless of George Washington.

In any case, here is a brief account of the incident alluded to:

"In 1753 Washington was sent as an ambassador from the British crown to the French officials and Indians as far north as present-day Erie, Pennsylvania. The following year he led another expedition to the area to assist in the construction of a fort at present-day Pittsburgh, Pennsylvania. Before reaching that point, he and some of his men, accompanied by Indian allies, ambushed a French scouting party. Its leader was killed, although the exact circumstances of his death were disputed. This peacetime act of aggression is seen as one of the first military steps leading to the global Seven Years' War. The French responded by attacking fortifications Washington erected following the ambush, forcing his surrender. Released on parole, Washington and his troops returned to Virginia."

Not exactly a glorious chapter in military history...

Washinton did prove, however, to be a pretty fine military leader as time went by, and he had the good fortune to end up on the winning side eventually in the American Revolution. If he'd been on the losing side, he'd almost undoubtedly have been hanged for treason.