Sugar not the enemy?

[Alexandra100]

Cat, testing every 15-20 minutes is a good idea and might well give a truer picture!

Or splashing out on a Libre sensor for a 24 hour over-view.

 

[LittleGreyCat]

We are all different.
I have extended Dawn Phenomenon.
BG starts a slow climb around midnight and seems to carry on through the morning.
Coffee, cream and butter does not lower this and can increase it.
Exercise (especially vigorous) can push up BG even higher.
Sometime after noon insulin seems to start working and then my BG usually comes down to a lower level than my morning fasting reading.

As others have suggested, you might be getting a short spike until a delayed insulin reaction kicks in and brings you down below your DP levels.
Without knowing how high the spike is, it is impossible to guess if kicking your pancreas first thing in the morning gives more benefit than leaving it alone.

Again as others have suggested, a Libre can give you a much clearer picture of what your body is doing over a 24 hour cycle.
This helps you to both understand and plan.
Or in my case leaves me totally confused about what my body is doing and why.