there are several authors who have maintained that the soul is co-eternal with god.
I came across one of them by Google today.
The Souls - Their Relation to Brahman
I am neither eastern orthodox nor roman, however I suspect that this is the type of theology that they have, too. There is an important concept of union with God and the denial of self in the gospels. This could be very similar to your ideas about being co-eternal with God, however it is not usually thought of as a universal trait but as something which must be seized upon by the individual.
As for 'Brahman': it is difficult (for me) to argue which Christian terms would closely match 'Brahman'. It will vary from Christian to Christian how they think about Christian terms. I would guess 'Heavens' or 'Glory' to be Brahman usually, not 'God'. God is often claimed to be the creator, however the heavens pre-exist creation. So does glory. In a person who thinks of God as the physical creator, then Brahman most closely matches Glory or Heavens; but in a person who thinks of all physical things as existing within God then God is a closer equivalent for 'Brahman'. There are caveats, too.
Here is one caveat: All catholics and all protestants are probably familiar with the scripture which says "In Him we live and move and have our being." This could refer to physical creation, and most people think of it that way. It may not. It may refer to the life in Christ which is a concept of union and leaving one's old ways behind. My point about this is that it depends upon what catholic or what protestant you are talking to whether they have a Brahman equivalent.
Also it is common for speakers to claim God creates the physical universe, however in Christian NT writings this is not necessarily a closed case. You cannot know what a Christian thinks about this, and their minds can change about it over time, too. God definitely creates Christianity, but that is not a physical creation. God creates Judaism, but that is not a physical creation but a moral one and a cultural one. Does God create the physical world? That is a gray area.
If God does create the physical universe then definitely neither God nor Heavens nor Glory are equivalent terms to Brahmam which implies no creation, however if God is the creator of Judaism or of Christianity and not of the physical universe then it is easier to consider some catholic terms as equivalent to Brahman. If the universe is simply a subset of God or is God then there is a similarity with Brahman. There are catholics and protestants who consider the universe to be either God or a subset of God which makes God sort of similar to Brahman in their case. That is true, but the Christian scriptures can confuse you about this. They seem to refer to God and Heavens separately in their terminology thought they also seem to equate God with heaven. Is God heaven? Is God the creator of Heaven? Does God create God? It is difficult, as I pointed out, to definitely say that there is a Brahman equivalent or isn't. There is, depending.
And recall what I said in the first paragraph about co-eternal. That requires much less exposition. Its fairly straight-forward. The main difficulty is in determining if there is an equivalent to Brahman.