This happens to me off and on - I know through my local low carb group that it also happens to folks who are not diabetic . For some of us, me included, it's linked to a sharp drop in BG followed by an equally sharp rise which seems (in my case anyway) to be the start of dawn phenomenon. It also goes along with nightmares and heavy (really heavy) sweating.
I can't explain the reason for the sudden fall (although I'd guess my liver is up to something) - and there seems to be little or nothing in the literature about it. If anyone has found anything, please link it here. Before widespread CGM use (and in particular Abbott's free CGM trial) I don't see how I could have detected it. By the time you wake up properly and test, the fall is over and BGs are climbing.
My A1c has been around 36 for over four years and I rarely get a fingerprick reading anywhere above 6 these days. Until the CGM trial, I had no reason to think it was linked to BG in any way. I tend to think whatever it is has an impact on BG, rather than my BG itself being the cause.
I'm attaching a CGM graph from a non-diabetic individual that shows the 3am BG fall very well.