Waking glucose levels

Welcome to the Forum. A reading of 7.8 mmol/L upon waking is in reality too high, but it's early days and being on metformin may take a few week to become more effective. It might be a case of wait an see what happens as one single reading on its own is not sufficient to draw any conclusions from.
Having a B/G meter will mean that you can see what your B/G reading is before a meal and then again 2 hours later, so that from the reading you can see what foods 'spike' your reading and those that don't.
The LCHF diet is a ver good means of controlling B/G for a Type 2 diabetic and you may want to consider this as a means of gaining control of your diabetes as many do with great success.

That isn't a bad level at all, well done! To answer your question, it can take a couple of weeks for lower numbers to appear, Metformin actually only lowers levels by a small amount - and 4 tabs per day is maximum dose. Paying attention to your diet can do more for you than Metformin will, and it certainly sounds like you're on the right track.

I wouldn't worry too much at the moment about your waking level, which isn't too bad as @ladybird64 has already told you! Your liver is programmed to give you a helping hand in the mornings (aka Dawn Phenomenon, or liver dumps), so you have less control over your glucose levels at this time because of this. Watch and try to reduce your before and after meal levels first as you have more control over these. Waking levels will eventually come down but generally after you've got the mealtime ones under good control.

And yes, your body does need some time to get used to its new regime - low carb can work wonders but it's NOT an instant fix, and you'll discover in due course that all sorts of other things (illness, infection, stress, some medication, etc) may adversely affect your glucose levels. I would consider extra metformin only as a last resort, as the right diet will generally be much more effective. If it doesn't work then extra medication would probably be the way to go, but your GP will advice you if such extra help appears to be necessary.

Robbity

I would just like to add that the fasting level is the last to come down so be patient carry on and you will get there. I actually found doing intermittent fasting and low carb helps significantly to reduce thee fasting reading.