Tom Brown proves that this is certainly possible, but then he has been doing it his entire life and has the extremely broad skill set to pull it off.
I have always had the same interest and have worked on some of the skills necessary but haven't been able to practice any of them enough to go out for a week (though I
might do it if I took a fall-back kit with me).
Some of the skills I have or need to work on are fire starting, identifying types of tinder, making a fire drill, identifying rocks that could create a spark, making cordage for the drill, making a cutting tool sufficient to create the drill board, etc. It is really a sequence of skills, many of which have predecessor skills required as this list shows. I'd encourage practice, practice, practice if you don't have these mastered.
Same for making traps, identifying wild edibles in your region, making fish traps or trotlines, etc. for food sources.
Are you concerned about purifying water? That's another area where any head knowledge I have has NOT been translated into practiced skills.
There are just so many aspects to this. I wish like anything that I had had a "grandfather" to teach me these skills when I was a child, like Brown did, and the opportunity to grow up practicing them far more regularly than I did. My family thought I was weird enough even from the little I did.