In order to respond to the prompt with a direct, concise thesis, I recommend "flipping" the prompt into a sentence starter. A strong thesis could begin, "Islamic civilization spread to encompass such a large empire through _________."
Although I don't have the exact documents you need to reference in your DBQ, there are some overarching ideas that will likely guide you in the right direction.
Religious and Political Conquest
As with most any civilization, Islamic civilization was significantly spread through military power. Strong armies, as well as a strong Muslim belief in spreading the faith, led to the conquering of many surrounding areas and lands.
While religious fervor was sometimes expressed through militaristic action, it could also be used for peaceful conversion. This brought many people (and their lands) into the empire.
Islamic civilization was also known for having strong governments. These governments kept the empire stable while also taking care of their citizens. Islamic governments were also generally tolerant of the ways of life of the people they conquered, so rebellions were less of a threat.
Islamic civilization was highly advanced in science, medicine, and engineering. This provided for better transportation, infrastructure, and care for the citizens living within the civilization. Better engineering also means more effective military operations and connections between far parts of an empire.