R.R.
As long as your son is comfortable being alone, I would not worry. This is just how some people are. We don't need to push anything just because the rest of the world does it that way. At this age, kids still play parallel than with each other. My son (also only child) too likes company of adults than other kids, most likely because his verbal and cognitive skills are way beyond his age. Sometimes, he comes across as a wise grown-up than a child. May be your son is also very insightful, keen observer, and perceptive?
My son is also mostly raised at home with us and grandparents, never went to day care. And did I mention that his bed is in our bedroom and I am okay with his sneaking into our bed any time he wants to. He would not even enter other people's homes until age 3. Now he is considered by far quite a gregarious 5.5 year old.
Just let your child be who he is and he will find his own way. And, one to one play dates is a good idea but without pushing him or making him too conscious about it. And, please do not label him as 'anti-social' or any other such labels. It is all in our own eyes how we see things not how things truly are. Once we lock our kids into certain labels, it is as if we expect them to behave that way such as saying he is 'shy, which is a very negative label.
Your child is cautious and that is a great quality to have as he will choose things wisely in his life not because somebody said so. He simply needs more time to warm up and should be supported for that not labeled for not meeting your expectations. I recommend reading books Between parent and child by Haim Ginot and how to raise your highly spirited child by Mary Sheedy Kurcinka.
Best,
-Rachna