There is no doubt that almost all musicians have influences that they carry with them throughout their careers. I say, “almost” to be on the safe side. You never know, there may be a famous musician somewhere who grew up with an instrument but had never heard any music. I would say that in that case, his influences would come from nature. Ordinarily, when any musician takes up an instrument for the first time, they play what they know. They try to reproduce what they have heard.
No one sets out to immediately establish a new theory of music, new chords, new scales, etc. Just the idea of that happening is silly.
This is true even for the greats. The great sax players, 'Trane, Bird, Pres, I can guarantee to you that their first efforts were in imitation of music that was familiar to them, and I can also guarantee that it was awful. It's hard as hell to get a decent sound out of a sax. Everybody who has ever tried will tell you that. They also learned some theory and started practicing scales. They all had other musicians that served as influences, but I don't know enough about saxophone music to have opinions about that.
Jerry Lee Lewis developed an interest in the boogie woogie piano. His method of studying was to listen from outside the building to professionals entertaining in a bar, and then go home and figure out what they were doing. That's not typical, but maybe it is pretty typical after all. I never had a guitar lesson. I just listened to records and then figured out what they were doing.
Guitar players! Now that's a group that I am more familiar with!
Most guitar players display their early influences forever. I think that it was B.B. King that admitted in an interview that, “we're all playing T. Bone music.” (T. Bone Walker) Even Albert King would probably admit that, although he comes as close as anybody to having found his own way in the musical forest. He was working on a trash truck down south and got the idea that people were making money just playing music. That seemed easier, so he figured he'd give it a go. He got a guitar and tuned it up, without any help, mind you. He tuned it so that it sounded good to him. Then he learned to play melodies on it, and found a few chords that sounded like the records that he had heard. Albert had an immediately recognizable sound, but he had heard many, many blues records before he took up the guitar.
Even someone as great as Jeff Beck had influences. At this point in his career, everything that he plays is Jeff Beck music. He has a style that can be spotted many miles away; when you hear him play, you know that it's him immediately. He is one of the few who has the distinction of playing in a style that no one else can duplicate. Jeff is a humble man, and he has always been happy to discuss his early influences, who were all of the serious pros that played on those 1950s rock records, perhaps especially the rockabilly records. He still sits in with bands that play OG rockabilly, and he kills it.
We know Jimi Hendrix almost entirely from his mature style. During the period of his popularity, there was no one else who sounded like that, or could duplicate what he was doing. We know very little about his early life, musically speaking. He was cryptic in interviews, so there were few clues. It's not hard to figure out what kind of music Jimi grew up with. That would be a combination of everything that was on the radio in Seattle, a very cosmopolitan city, plus a sprinkling of blues and jazz.
Below you will find three songs from guitarists that I would say almost certainly influenced Jimi's playing. I stopped at three because I didn't want to start guessing. I'd love to hear from anyone who had additions to the list.