It will take some time and work, but the physical change for me has been as important as the mental. Ok, not as important, but follows close behind, especially as I believe in the deep interconnection between mind and body.
I've been sober almost 5 months, I've lost almost 15pds from a pretty in-shape 190pds to begin with. I'm in the best shape of my life at 41 years old. My sleep is deep as can be. I have patience, energy, focus etc.
Others may feel differently but for me really committing to my fitness goes in step with my sobriety. One fuels the other - ie I'm not getting up for a heavy weightlifting session at 5:30am if I'm hungover etc. And I think by committing to a fitness/diet program (I intermittently fast as well) I see results that I can correlate to sobriety that otherwise may take longer or not manifest themselves at all.