Here is a passage from St. John Damascene:
But
if we say that the Father is the origin of the Son and greater than the Son, we do not suggest any precedence in time or superiority in nature of the Father over the Son(for through His agency He made the ages), or superiority in any other respect save causation. And we mean by this, that the Son is begotten of the Father and not the Father of the Son, and that the Father naturally is the cause of the Son: just as we say in the same way not that fire proceedeth from light, but rather light from fire. So then,
whenever we hear it said that the Father is the origin of the Son and greater than the Son, let us understand it to mean in respect of causation. And just as we do not say that fire is of one essence and light of another, so we cannot say that the Father is of one essence and the Son of another: but both are of one and the same essence. And just as we say that fire has brightness through the light proceeding from it, and do not consider the light of the fire as an instrument ministering to the fire, but rather as its natural force: so we say that the Father creates all that He creates through His Only-begotten Son, not as though the Son were a mere instrument serving the Father’s ends, but as His natural and subsistential force.
This is exactly what I mean when I say the Father is greater than the Son, that the Father alone is unbegotten, while the Son (alone) is begotten. He goes on further down the article:
All then that the Son and the Spirit have is from the Father, even their very being: and unless the Father is, neither the Son nor the Spirit is. And unless the Father possesses a certain attribute, neither the Son nor the Spirit possesses it: and through the Father, that is, because of the Father’s existence, the Son and the Spirit exist, and through the Father, that is, because of the Father having the qualities, the Son and the Spirit have all their qualities, those of being unbegotten, and of birth and of procession being excepted. For in these hypostatic or personal properties alone do the three holy subsistences differ from each other, being indivisibly divided not by essence but by the distinguishing mark of their proper and peculiar subsistence.
The Father’s existence is “prior” in the order of both of the Divine processions. This is not in a temporal sense, as the saint points out, but more in a logical or causal sense (and even then these are mere analogs).
I recommend everyone read the entire entry by St. John of Domascus for deeper understanding:
ccel.org/ccel/schaff/npnf209.iii.iv.i.viii.html
Christi pax.