I read the title and the answer is "no."
There are so many other causes of childhood depression (wrong school system, etc.) and the fact that childhood depression existed long before desktop computers of any kind existed that no, social media, as such, is such a small part. Indeed, social media is sometimes the only connection left a depressed person has with the world at large (and if this is you, seek help *right now*^`1) that removing access to it (because parents are going to only read the title) would be harmful.
--
BMO
1. That was me back in 2012. The only things I did were food shopping and going to the pharmacy. If that. But not enough. I lost a bunch of weight due to anorexia (anorexia is not just teenage kids with body image problems, it's also adults or anyone else that just doesn't feel the need to eat). While losing weight this way was effective, it's not recommended by me. My world shrunk to my apartment and the only connection with the outside world was my computer and my property manager who insisted that I come over and sit around the barbecue roughly every Saturday and he wouldn't take no for an answer. (he had a key, of course)
About that. I was pretty good at putting on the mask, so nobody would know that anything was wrong, just that I wasn't around much.
By the time December rolled around and my brother rescued me, I was an almost-suicidal mess and didn't care what happened to me because I didn't think anyone would miss me. Steve probably kept me alive long enough for that to happen. Without the two Steves (my brother is also named Steve), I'd probably be dead from the heart attack in Feb 2013.
Which leads me to today. I am still alive, and I have an actual life again. It took a lot of work and a lot of visits to the head shrinker, but I am mostly functional and/married/ to a wonderful person who doesn't think I'm as awful as I think I am.
The tl;dr of this footnote is that life changes and if your only connection to the outside world is social media, you are in a depressive episode and you need help immediately. You cannot drag yourself out of it alone. But if you get help, you will get the time for life to change for the better (because it can't get much worse). Help doesn't have to be professional help, but it can be a friend or your local DBSA. Google that organization and find a group close to you and go.