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The Calvinistic position, traditionally, is not that the Son is (as stated in the question) 'begotten of the Father before all ages', but, rather, that the Son is :
eternally begotten of the Father.
A very informative article by Benjamin W. Swinburnson states it thus :
This doctrine, as classically defined in Reformed theology, states that God the Father, by an eternal personal act, by necessity of nature, generates the person (not the essence) of the Son by communicating to him the whole indivisible substance of the Godhead, without division, alienation, or change.
And his article, in detail, argues that John Calvin did so teach.
The begetting, so taught, is a matter of an eternal begetting, without beginning, without ending, outside of time. It is an eternal matter - between the Father and the Son - and is fulfilled in one Spirit.
Upvote:2
From Wikipedia (https://en.wikipedia.org/wiki/Calvinism#God):
Traditionally, Reformed theologians have also followed the medieval tradition going back to before the early church councils of Nicaea and Chalcedon on the doctrine of the Trinity. God is affirmed to be one God in three persons: Father, Son, and Holy Spirit. The Son (Christ) is held to be eternally begotten by the Father and the Holy Spirit eternally proceeding from the Father and Son.