Yes. The Son existed whensoever the Father existed and thus the Son is co-eternal with the Father, and likewise the Holy Ghost is co-eternal with both because the Father does not beget the Son by will, but by nature, and the Father's nature was perfect from eternity, and the action whereby the Father produces the Son is not successive (because otherwise the Son would be successively generated, and this generation would be material, and accompanied with movement: which is quite impossible).
Athanasius declares that "all the three persons are co-eternal with each other."
In time there is something indivisible--namely, the instant; and there is something else which endures--namely, time. But in eternity the indivisible "now" stands ever still, as we have said above (Q10, A2 ad 1, A4 ad 2).
But the generation of the Son is not in the "now" of time, or in time, but in eternity.
And so to express the presentiality and permanence of eternity, we can say that "He is ever being born," as Origen said (Hom. in Joan. i). But as Gregory [Moral. xxix, 21] and Augustine [Super Ps. 2:7 said, it is better to say "ever born," so that "ever" may denote the permanence of eternity, and "born" the perfection of the only Begotten.
Thus, therefore, neither is the Son imperfect, nor "was there a time when He was not," as Arius said.