I think we’ve discussed this before. I am able to have plenty of green vegetables within a 20g NET allocation (Brussels sprouts, cauliflower, broccoli, lettuce, etc.) and even some berries due to the high fiber count. If you are doing TOTAL carbs then that is harder. Work out what carbs are causing your overages. If you are not logging food, it sounds like you need to.
I’m not sure I’ve seen any evidence for this anywhere on these forums. It is true that as you improve your insulin sensitivity you can increase your carbs but that is more likely measured in months or years depending on your degree of metabolic derangement. Becoming “keto adapted” - is not really a thing. You get into ketosis (burn fat to make ketones) fairly quickly which is separate from becoming fat adapted (body expects ketones as a primary fuel source and uses them efficiently) which can take weeks. Achieving neither is likely to have an impact on your base level of carbs that will keep you there. Fasting could accelerate things but potentially at the cost of metabolic slowdown which will cost you much more in the long term.
If you are not damaged and are just doing this for prevention/longevity, you don’t need to be at 20g anyway and could achieve ketosis at a higher level from the start.
From most evidence around here, this is usually counter productive. People try to increase caloric deficit, fast too early, lower the fat before being fat adapted etc. to “accelerate” things and they rarely, if ever seem to work and often create stalls or metabolic slowdown.
Your body is in control of this journey not your mind no matter how much you want it. Realizing this will help you stop over-thinking things and get on with other things in your life which are surely more important.