The first week was the hardest for me. On day three, I would start climbing the walls, as both my AV and my physical body started reacting to the absence of alcohol in my system. This is indeed where a huge reservoir of mental strength is needed, But Scott and others are right. Don't sit there and dwell on NOT drinking, but distract yourself. Your AV doesn't like that because it needs to keep you engaged, and it does that by injecting thoughts of alcohol into your mind. Distract yourself, and put them out of your mind.
On day 5, it was the worst, but it was also the end of my life of drinking. It coincided with me accepting and embracing that I could never drink again, and my distraction of choice turned out to be AA meetings every night for 90 days. This is what got me through my "witching hour." And if I made it through that by being with people celebrating sobriety, I wouldn't drink that day.
Eventually, you no longer need these props. If you commit to never having another drink, you begin a new life where your AV is still in the background, but is reduced to ineffective noise that you can simply ignore.
If the AA program is not your cup of tea (it wasn't mine), you can just use the fellowship as a distraction until you get that voice in your head under control. For me, the AA program did not apply to my alcoholism, but the people were indispensable. You may find some other distraction that works better for you.
Your goal is not necessarily to become stronger but to break the cycle of addiction so that you don't have to be stronger. Good grief, if sobriety was a life of constantly engaging my AV, I never would have made it. You need to cut your AV off at the knees, and that is what happens when you break the cycle by not drinking.
You will still need to be alert, because your AV will become sneakier and more devious. When you think you are out of the woods, your AV will appear again and make you think you are well enough to drink normally. This is where many fail. When you think you are well enough to have one little drink, you are about to slip back into the nightmare of addiction. Don't fall for this.