Can "one" do this? There are lots of self-taught guitarists out there, some of them respected professionals, so it's possible in principle, and arguably it's easier today than ever before, with boatloads of instructional videos on Youtube, reams of free practice material on ultimate-guitar.com, games like Rocksmith etc.
Can you do it? That depends on your talent, your drive, and what else in going on in your life. You'll have to put in the hours, probably more so than someone with a teacher to guide them, and you should be careful and self-critical so you don't pick up bad habits.
Is it the best way to proceed? Depends on your circumstances - the availability and affordability of competent teachers, your personality and so on. I would recommend taking some lessons to at least put you on the right track, but if that's not an option... put in the effort to learn by yourself, and good luck!