He always has existed and He never was created, as He is not like His creation, nor similar to it, in any way.
The prophet Muhammad (peace be upon him) explained the devil would come to a person and ask them questions about creation; "Who created this or that?" to which the reply would be; "Allah" until he would ask; "Who created Allah?" At this stage the prophet advised us to drop this train of thought. Obviously, God - the real God, must be eternal and not have to be created.
The Quran tells us:
Allah! La ilaha illa Huwa (There is no god to worship except Him), the Ever Living, the Sustainer and Protector of all that exists. He doesn't get tired and He doesn't sleep. Everything in the universe belongs to Him. Who then, could intercede between Him and his creatures without His Permission? He Knows everything about them and they have no knowledge except as He wills. His kursi (stool or chair) extends over the entire universe and He doesn't get tired of guarding and preserving it. He is Most High, the Most Great.
[This Verse is called Ayat-ul-Kursi.] [Noble Quran 2:255]
This verse truly presents the comprehensive representation of God in a way without trying to define Him by comparing Him to His creation, but rather as being the Absolute in all of His Attributes and Characteristics.