When I was diagnosed my HbA1c was 114 but by switching to a LCHF diet, exercising more and losing weight it was back in the normal range 5 months later (but on just, at 41) and I've managed to keep it below pre-diabetic level since. That doesn't mean that the answer to your question is 5 months because we're all different and that's only what I managed, plus I didn't have so far to go as you.
What I found helpful was testing first thing in the morning and also two hours after our evening meal and recording the results in a spreadsheet. When I had enough readings I inserted a graph showing the 7-day moving averages for fasting and post-prandial, and this showed me that by BG was on a downward trend and that what I was doing was working. I'm still doing it and now have sixteen months' data. My moving average started at 9.2 and is at 5.4 as of today.
I did statistics at college and have worked in data analysis so once I had a set of numbers I was in my element.
Martin