Sometimes you can never feel as lonely as in a group of people who all know each other, or may appear to.
“Joining “ is not for everybody, something less full on may be easier.
Just bear in mind, you can be alone and enjoy your company, there is nothing wrong with that, but trying activities which appeal to you may well result in meeting people with a similar outlook.
I would take it gently, you are unlikely to firm close friendships at least not immediately. Just smile, be friendly, take an interest in others and remember that there are many people who feel just as you do - if you were to scratch the surface.