First, one has to make clear which of the many gods is meant. Because theistic people in different religions speak about many different gods: The Olympic gods from the time of Homer, the Egyptian gods, the Vedic gods, the Hinduistic gods, the monotheistic Jewish and Christian god named Jahwe, and many more.
Secondly, in Christian theology the attempt to prove the existence of god by logical reasoning alone - withount any empirical base - uses the definition
god = a being than which nothing greater can be conceived (lat. aliquid quo maius nihil cogitari posset)
You find the attempt to prove the existence of such being in chap. II of Anselm of Canterbury: Proslogion. In short, Anselm reasons indirectly: In case such being misses existence then one can conceive a greater being, namely a being which in addition to all other properties also exists. Following the line of Anselm's argumentation one can easily derive that the being in question has also created the world, otherwise one could imagine a greater being. Anselm's argument is named the ontological argument.
The argument was already questioned by a Christian monk, Gaunilo, in a brilliant controversy with Anselm. A reference is http://www.iep.utm.edu/ont-arg/ . The main counter argument has been given by Kant: Existence is not an additional property.
Thirdly, a certain type of argument focus on proving that the universe has been created by a creator. That's the argument from cosmology. Apparently, it has an empirical premise, namely the existence of the universe taken as a fact. The argument is due to Leibniz. His reasoning in short: From his premise that all things have a sufficient reason Leibniz concludes the existence of a first reason of the universe, which he names god - see Gottfried Wilhelm Leibniz: Ueber den letzten Ursprung der Dinge (in German).
Today, all attempts to prove the existence of a god or of any of his doings by philosophical or scientific means are considered controversial.
Note. I changed my last sentence because of the comment of @James Kingsbery