I'd advise first working to overcome social anxiety, and that's what Dr. Richards has said in the groups.
A quick look at the most popular thread on this forum: "So anxious around the opposite sex? ugh why? please anyone help?" with almost 30,000 views.
So, there you go! Yep, we all want relationships, well most of us. And that's a natural thing. I should point out, relationships here, any kind, doesn't matter your sexual orientation although the original poster used the phrase "opposite sex" I think we can easily spread this to any kind of romantic relationship.
So yes, we all want relationships in our lives, right? And social anxiety affects that tremendously. A relationship involves every part of life - acceptance, confidence, the ability to communicate, assertion, ... ... . I mean the real question might be, what DOESN'T a relationship touch on in life? So then obviously if you have social anxiety disorder, it's going to be hard to have a healthy relationship. And for men here, as culture and society often require the man to take the initiative, social anxiety can really affect you in this area. I don't want to downplay the frustrations women also have in the relationship area, dealing with social anxiety. Quite often, though, this is a huge sore spot for men on the forum and in our groups.
So, we don't really want to push off having relationships. There's such a natural desire for them. You can't just turn that desire off. And there's usually a question here, what can I do? What do I do about getting a girl/boy friend? Why not get yourself into a better position to be able to deal with and handle a relationship before getting all balled up about not having one? Work on overcoming social anxiety first. Work on the therapy. Then open yourself up to dating. Yes, the dating won't be perfect or easy at first, but SURPRISE - it's not easy for anyone. That's life. But when you're struggling with social anxiety, the relationship you are running after and might catch will also involve all these SA problems you're dealing with. Get to a place where you are emotionally and mentally healthier to be able to at least face the normal challenges of a relationship.
I'm not telling you to postpone your life forever. Just don't get all worked up on this one point. Don't hate yourself because you define it that way, a single person. Do the therapy, and the skills you gain there will help you better navigate dating and better handle healthy human communication that is necessary for any healthy human relationship.
Advice for just dating or relationships that doesn't involve first dealing with social anxiety is, in my opinion, not very helpful.