Yes, I have heard this claim before. Where does it come from?
The belief in the eternity of God comes from Scripture and creed and the writings of the saints.
In the book of Genesis, God creates the world. The world has a first day, but God was there already, before the first day, before time, that is, in eternity.
In the Gospel of St. John, our Lord says “Before Abraham was, I am”, with an interesting mix of verb tenses that to my mind strongly suggests an eternal point of view.
The Niceno-Constantinopolitan Creed says that Jesus Christ was “born of the Father before all ages”, i.e. before time began.
Here are the first three quotes from the saints I found on the eternity of God. More could be found, I’m sure:
“This is the New Song, the manifestation of the Word that was in the beginning, and before the beginning. The Saviour, who existed before, has in recent days appeared. He, who is in Him that truly is, has appeared; for the Word, who ‘was with God,’ and by whom all things were created, has appeared as our Teacher. The Word, who in the beginning bestowed on us life as Creator when He formed us, taught us to live well when He appeared as our Teacher; that as God He might afterwards conduct us to the life which never ends.”
Saint Clement of Alexandria (c. 150 - 215),
Exhortation to the Heathen
“omnipotence and eternity are the possession of One only, for omnipotence is incapable of degrees of strength or weakness, and eternity of priority or succession. In God we must worship absolute eternity and absolute power”
Saint Hilary of Poitiers (c. 300 - 368),
On the Trinity
“everything that begins to be and then ceases to be begins and ceases when it is known in thy eternal Reason that it ought to begin or cease–in thy eternal Reason where nothing begins or ceases.”
Saint Augustine of Hippo (354 - 430),
Confessions