God only knew

Even if your prose is in the past tense, not everything the narrator says must be cast that way. For example, in:

"God only knows what John was thinking when he decided to rob the bank."

clearly, God's omniscient understanding of John's incomprehensible motives is ongoing in the present of the narrative, even if John's actions are in the past. Actually, even in non-fiction and common speech, "God only knows" is frequently used to describe past events: "What where you thinking??? God only knows!!!"

This doesn't necessarily apply to every common expression or even other examples of this expression. I would look at each on a case-by-case basis.

What about something like:

Back then, God only knew what was going through our minds.

does this make sense?

This is an example of what is really an idiomatic expression, one which is not at all dependent on one's belief in a deity. But its basis is, of course, the traditional Christian God concept, in which, as mentioned above, God's knowing is in the present tense.

If one were to use a similar construction with non-supernatural beings, one probably would use either past or present tense, depending on whether or not they still know.

The "God only knows" expression is rather trite and overused, so it might make better prose to construct it in past, rather than present tense, just to be less so.

I believe it rests on the premise that God is all-knowing, all the time. So anything He ever knew, He always did know, knows now, and will forever know. It's similar to the quote "before Abraham was, I am." While that conflicts with tense in English syntax, it is seen as a correct statement because that is His forever state of being. Consider it the 'perfect tense' form. So, regardless of when an event took place, God only knows what happened.
Also gives the impression that everyone else has forgotten (or died) and God is the only one left who really knows what went on. Also that He's the only unbiased source; the only one with a purely objective view of things.

god aint rel