That's humorous, to "think of God atemporally?" I can't do anything atemporarally.
But I do know what time is -- or at least I experience it. And while I know God is eternal, I do use the notion of "non-eternal" to remind myself of what God is not: God is not non-eternal! Of course I can just strip the double negative like English teachers, like my wife prefer. But sinner that I am I have to fight sin creaping into my thoughts. Wouldn't it be comforting if God changed by adjusting to me??? How convenient. Point made...
Eternal, Everlasting, Eternity... these are words Christians have used -- in various ways -- throught the centuries. Always using them meaningfully and purposefully. Yes, all such language used temporal sequence. But using words that say what is "not" can also be done in time, sequentially. Dionysius wrote that eternity is time at rest and time is eternity in motion. Consider (a temporal act) "eternal life" for a moment. For humans we can, in Christ, experience eternal life by grace, what the Son of God experiences by nature. Such experience does not mean being frozen--ceasing to live. Such participation (1 Peter) in the divine nature is eternal rest and eternal becoming, and eternal communion--koinonia! But something else has stopped. We don't; but it does. And the "it" is the corruptioin of time by death of sin.'
Fathers of the Church, descriptively (and carefully) even spoke of us becoming--by grace (not nature)--"everlasting" too, as God is. That means that one of the defining things about us will be being-beyond-eternity. That is, sharing via gifting by God, in what God is. (Again, 1 Peter.)
You said, "This very state of affairs--the inability to conceive of atemporal existence--is what makes me think God doesn't expect us to get around temporality." What I think is important is to realize that for those who did not speak Latin, who were not faced with dealing with Augustine's notions of predestination, the challenge was merely to develop ways of addressing sin, corruption, and salvation. For doing this speaking of contrasts was important: eternal means not subject to corruption, etc. For God we have to have *some* way of speaking of God being *beyond* eternal, then. Redeemed creation, that is redeemed by a power beyond themselves (whether men or angels) can be eternal. And God is certainly beyond that. So "everlasting" was used sometimes, and expressions such as "pre-eternal" too. They achieved the need that they were faced with. Good enough. But even then it was realized and commented on that while such word-constructions did the job in one way (as analogies do) they failed if pushed to far (as is true of analogies).
Non-Latin speakers faced complicated notions of time later, when conflicts and debates with Islam happened. John of Damascus is noteable.
As to what you said about whether God requires us to do something mentally challenging, to "conceive of atemporal existence" (which btw is a contradictory phrase -- see Gregory Naz "Orations") -- that's not relevant. Feel off *that* hook. As above the hook we ARE on is sin, corruption, and salvation by grace. And then for THOSE topics of eternity (beyond time) and everlasting (beyond creation) and pre-eternal (same) are good for us because they describe in a POSITIVE way a road-map of where God has prepared a place for us to go. And using those Maximus or Dionysius even said that sinful created man could even become (by Grace) "uncreated" and "pre-eternal."
To God be the glory!
- B in Chi.