Like most innovations in history, when we look closely at them we discover that they are steps along a path, some bigger than others.

Papal advocacy of what became the first crusade was built on the successes of the 11th century Reconquista wars against the muslim Moors in Spain. These wars were advocated by Popes such as Alexander II and preached through monasteries and bishoprics in areas we now call France and Italy - thus we see important battles fought with large contingents of 'foreign' forces. These preachings include such crusade tropes as indulgences.

The Reconquista, if you could refer to several centuries of conflict as one 'thing', had been in progress for several hundred years by this time, effectively since the Carolingians and with the advocacy, passive or active, of the papal curia. It had a long lineage tied into theocratic monarchy, and the imperial defence of Christian lands.

When we look at this era of theocratic kingship - the Carolingian period through 12th century - there is complexity in sifting out temporal from religious motivations on the part of king and pope, if even possible.

Now, before we get excited that Alexander's involvement in the Reconquista was then first!, we would do well to remember that Alexander was consulted by the Normans in advance of their invasion of England; Alexander gave his blessing to them.

Papal sanction of wars in the name of Christianity was not infrequent, and it did not begin with the first crusades.

The Crusades were not seen (nor should they be) as a series of offensive wars against Muslims.

11th Century Christians had witnessed the expansion of Muslims into Christian lands by way of force for some 400 years prior to the launching of the First Crusade, which had as its aim the defense of the Eastern Churches and the conquest of Jerusalem/the opening of the Holy Lands for pilgrimages. In AD600, about thirty years after Mohammad was born, Christendom was spread throughout much of Europe, the Middle East (through not just modern-day Turkey, Lebanon, and Syria, but through Baghdad to the coast of the Persian Gulf), and North Africa. By AD750, this area had been reduced to Europe and parts of Anatolia by way of Muslim conquest. Only the Byzantines in the East stood as bulwark against the Arab horde, and when the 11th century rolled around, they were under very real threat of being toppled, and with them the rest of Eastern Europe.

As to whether Pope Urban II was the first Pope to issue a call to arms in defense of Christendom: that's a difficult question to answer. Most would venture to say No, probably not. As /u/idjet pointed out, the Reconquista had been occurring for some time by the time Urban II preached the Crusade at Clermont, and prior to that there were wars undertaken with a degree of support - passive or active - of the Pope and curia. A significant additional example comes to mind with Pope Leo III, who crowned Charlemagne in AD800, and supported subsequent Frankish campaigns as a means of solidifying Papal autonomy. This itself was a continuation of policy from Charlemagne's father, Pepin, and Pope Leo III's predecessors Popes Zachary and Stephen II.