I've been seriously interested in Indian music for my entire adult life, and feel it's time to get an instrument of my own. Regarding stringed instruments, like the sitar, these things look incredibly complicated, with more strings than I can count. Any instruction I get in how to hold it, how to create notes properly, how to pluck the strings, hold the plectrums, how to tune it, and God knows what else, is going to be via the Internet. YouTube videos and various music blogs are all that will be available, as the nearest teachers are probably a thousand miles away from where I live, at least. Is it possible to become proficient on one of these instruments using YouTube?
I'd like to weigh in as a party-pooping naysayer, since any optimistic answer boils down to "Sure, knock yourself out." Actually, I jest; it's a wonderful goal and worth pursuing. I'm not sure how far you can get self-teaching, though, and you should be prepared that even "the right way," it would be a very long process (presumably, much longer "the wrong way").
(Disclaimer: Any knowledge I have of Indian musics is as an outsider, gained from a few textbooks and concerts. I hope someone with more direct experience can give better perspective.)
Yes, a sitar is a very complex instrument.* Aspiring students in the traditional guru-disciple system would spend a certain length of time just accompanying the master on the tanpura, which you just strum repeatedly, before being allowed to even touch a melodic instrument. For months or maybe years, the shishya would live in the guru's household, doing menial chores, cooking, cleaning, and sweeping, waiting for their chance at instruction. Perhaps this system simply got the chores done, and surely that was part of it, but meanwhile the shishya was immersed, 24 hours, in the music around them, and was internalizing the nuances and language of its conventions.
My understanding is that the guru-shishya system that I'm describing is largely in the past, and Indian classical music education has been opened up to large classes and more accommodating models. But it's important to know its tradition, and just how far you have to "catch up." Indian classical music has its own systems of structuring, analyzing, talking about every aspect of music from melody to rhythm. Within the Western tradition, you could switch from violin to oboe, or even to electric guitar, and you're just learning different mechanics. In switching to Indian classical, you have to build alternate structures to things you've learned since Kindergarten. Even explaining the concept of raga takes several iterations of misunderstanding ("So it's like melody?" Not quite. "It's like a scale?" That's part of it. "It's like baroque ornamentation practices?" In a way.)
Of course, maybe your goal is less lofty than to become a master. You certainly can learn the basic mechanics quickly enough to insert the sound of the sitar into Western music; George Harrison certainly did. (Though, note, he met his own limits and concluded "I'm not going to be a great sitar player ... because I should have started at least fifteen years earlier.")
So what should you do? First of all, try to find a teacher. You assume "the nearest teachers are probably a thousand miles away," but unless you're thousands of miles away from everyone, don't be so sure. Indian classical music has globalized quite broadly. By far the easiest way to start would be with direct personal instruction, even for a single lesson. Also, over the past couple of years, I've grown much more favorable to the idea of lessons over Zoom (or other telepresence); it's certainly "not as good" as in person, but far better than non-interactive resources.
* Though it’s not as bad as it seems, because there are only 6-7 strings that you actually play, and 21 or so that just vibrate sympathetically. Still gotta tune them, though.
Can you gain proficiency in the sitar via YouTube? Almost certainly not. At the very minimum, you will need someone to provide feedback on your efforts, and no YouTube video will get you that.
Does that mean you're cut off from learning to play? Again, almost certainly not. As long as you have a good internet connection that allows seamless two-way video, you should be able to find a teacher who conducts lessons over Zoom, Skype, WhatsApp, or similar. Extensive research (i.e., cursory googling) turned up the following sites:
... and many others. I cannot vouch for any of them personally, alas, but I don't see any inherent reason that online lessons wouldn't work.
Finally, don't be so sure that you can't find a sitar teacher within a few miles of you. Working professionals from India, Pakistan, Bangladesh, and Nepal are pretty common in most parts of the world—certainly in English-speaking countries. Some percentage of those play sitar on the side and might be happy to take on a student just as a way of staying in touch with the instrument themselves. Or those who have settled here for long enough might have a retired parent living with them who is an accomplished musician and who'd be delighted to pass on some skills.
In most large towns, there might be an Indian, Bangladeshi, or Pakistani community center somewhere around that might offer lessons, or at least, will have a notice board where you can put up a flyer asking about lessons. Failing that, you could go to a few Indian restaurants and ask the proprietors if you can put up a flyer. They'll probably say yes, especially if you offer to pay them. In university towns, graduate students from the subcontinent might be a good source of information, if not actual tutelage (though those on a student visa couldn't teach you for pay). The university website will have contact information for the South Asian students' associations.
I rather suspect finding an actual sitar will be harder than finding a sitar teacher. You can always buy one online, but without guidance, it will be hard to know whether you're getting a decent one. So talking to a teacher before spending the cash on a sitar is probably a good idea.
Finally, if you've been "seriously interested in Indian music", you must have attended performances? And hopefully become part of a community of listeners that way? Some of those folks would have suggestions for you, I imagine?
If one is a musician already, then it's possible to self-learn the instrument. The most challenging part of initial phases of sitar learning is (i) changing its strings and (ii) the tuning. A musician should easily be able to tune the instrument in about 15 minutes, even though there are more than a dozen strings to be tuned. Posture is only a matter of time. The tuning system in Sitar uses harmonics, and more the ear is developed for pitches and sensitivity for harmonics, better will the tuning be. Even playing a basic scale on a perfectly tuned sitar at different speeds is itself a satisfying experience! Sitar has a couple of frets absent, which means, in order to play those scales, those frets need to be moved by half note distance. In the beginning, 10 scales get used for basic lessons to give fingers the practice and feel for the note positions, which may take about an year to master.