I've seen a consistent rise in my BG from 4:30am on; however, the rise is slow at first and speeds up after I wake. "First foot on the floor" phenomenon The problem that makes it hard to track in my case is that my house is generally on the dry side and I dehydrate to some degree overnight most of the time. If I wake at 3am, or so, and take a big drink of water, I get more reliable numbers at "dawn," but many nights - and lately, most nights, I sleep through that point or, even when I do wake, I forget to take that water, in which case, my CGM slowly goes out of sync with my BG at around the same time that my BG is rising. When I wake somewhat dehydrated, I see as much as a 40pt difference between my BG on the meter and the CGM.
Sorry I can't give a better answer. What I can say, though is that my 'DP' is still somewhat inconsistent, though more in magnitude than in timing. I rarely have nighttime snacks anymore. What I have seen that affects it is NOT eating enough carbs at dinner (I need at least 15-25g carbs at dinner to get better morning numbers), and an evening 'low-carb' alcoholic drink - which usually results in less DP.