I can totally understand your situation as I've been through the same.
But you shouldn't lose hope. Starting a pet project is not as hard as you might think and it doesn't really have to be the "next facebook". Just start anything you think might help you learn on the way and go ahead. Once done, blog about it, about your journey while developing this app, what you learned, what inspired you and you will get your first audience. Post it on Medium, here on dev.to and if you have your own blog, post it there as well and who knows, you might get a job offer as well 😉
And about coming up with side projects, it doesn't matter if something is already done as long as your are building for learning. You see something, you like it? Create a clone of it. Look for stuff that's missing in it (nothing is perfect ever), add that too. And there is your new little pet project 🎉. Publish it on git and repeat...
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