But if you have normal interactions with people on a regular basis, you'll get invitations. They might be tiny or tentative or impersonal, but if engage with questions like "Can I talk to you for a second?" or "Would you like a sample of our new Teriyaki Chicken?" or even "Do you have the time?" you'll gradually open yourself up to more possibilities.
And I do think if you're not in any club (for sports or hobbies or whatever) it gets harder and harder to make friends the older you get (spoken like a true mid-30s person ;). I don't have kids or a dog, so the workplace is next to the best venue to meet new people.
TLDR: I don't think it's in any way rare or weird to not receive invitations if you don't already have a network of friends. This is a catch-22.
I'm not saying "you must do this, it is the only way." It worked for me at a specific place and time in my life, and that isn't a universal condition. But I don't think we are helpless. Modern urban life may be alienating, but it's not inescapable. If you find that you value human connection more than likes or RSUs or Game of Thrones, you can find a way to have more of it.
Learn a new skill and meet people.
That approach works great as long as you are currently getting invited to things. If it's been a year since the last time you were invited to anything, that's not going to solve your loneliness problem.