"I've tried it and it was awful"
You may have tried this already. A walk with nothing on, a shower without the speaker, and it was every bit as unpleasant as chapter 3 said. Restless, twitchy, reaching for the phone that wasn't there, and you concluded that quiet isn't for you.
Go back to Wilson's participants. They were asked for six to fifteen minutes, cold, in a bare room, having filled every minute of their lives up to that point. That's the hardest version of quiet there is, and it's roughly what you tried. A fifteen-minute walk with nothing on, after years of fill, is the shock experiment without the shock, and the fact that it was awful is what the study predicted.
Two things follow. The first is that the itch is the beginning, not the whole. Wilson's studies stopped at fifteen minutes and so did your walk, and neither found out what happens after, because the itch was the exit. In my experience, and this is observation rather than a finding, the itch is loudest in the first two or three minutes and quieter by five, and by ten something else has usually turned up, a thought that finishes or a thing you notice, and the last five minutes of a fifteen-minute quiet walk are nothing like the first five. You've only ever had the first five.
The second is to start smaller. Not fifteen minutes. Three. The walk to the car, with nothing on, four minutes, once a day. The itch will come and you'll be at the car before it's got going. Do that for a week and the itch is shorter, because the mind has learned that quiet minutes end and nothing bad happens in them. Then the kettle. Then the shower. Then, by the third or fourth week, a fifteen-minute walk that has the itch in the first three minutes and the drift in the rest.
The itch passes. It passes faster each time. And the awfulness you remember was the first five minutes of a thing you'd never done, and you stopped before the second five, and the second five is the point.