Yes.

The research is quite confusing. This is because the strongest version of the argument is not "your child uses social media, and that makes them depressed". The strongest version is more like "when a society mass adopts social media, this irrevocably alters the culture in ways that causes massive changes in mental health, most prominently among young girls, including those exposed to the culture who don't even use social media."

This means you get a weird effect where experimental studies of high quality - which are usually the best evidence, are expected by the strong argument to show zero effect.

Correlational studies usually show either a weak effect (stronger in young girls) or no effect (it's extremely rare to see a study showing a positive correlational effect, though).

And where you get the most juice is looking at population level introduction of social media studies like those discussed here: https://www.afterbabel.com/p/phone-based-childhood-cause-epi...

But even then it's very tricky, as those studies can't exactly be replicated, and we don't know whether changes will actually reverse the cultural artifacts