Thanks so much for your question about autism, social skills, and making friends. Before I answer it, I want to offer my support to you, mom-to-mom, and encourage you to take good care of yourself during this journey. Please learn from my mistakes. I became too focused on trying to “cure” my son and lost sight of the big picture. I didn't pay enough attention to my marriage, my younger son and, most of all, my own mental, physical, and emotional well-being. So please make yourself a priority and surround yourself with caring people.
With that being said, I totally understand how important it is that your son develops social skills and makes friends. At three years of age, however, all children (autistic or not) still engage in parallel play, meaning they play near one another but don't necessarily interact with one another. As a former preschool teacher, I saw this all the time with that age group. Kids, for example, would sit in the sandbox, each one happily doing their own thing and not even being aware of those around them. Then, when they got to be 4 and 5, they began to realize that those were other human beings—great sources of fun, adventure, and friendship. So, if your 3-year-old seems disinterested in other kids at this point, it's no cause for alarm.
When my son was 3, we started building the foundation for successful social skills and solid friendships by taking him to speech therapy twice a week. Like many kids with autism, he needed help with articulation (pronouncing his words correctly) and social communication (making eye contact, reading facial expressions, and understanding body language). If he were to have friendships in the future, he needed first to develop these skills so others could understand him and others could understand him. When I was teaching preschool, I dealt with autistic children who hadn't received speech therapy, and it was extremely frustrating for everyone involved. Early intervention services are so important and not getting speech therapy during the younger years is definitely a missed opportunity.
As I mentioned in my article, the co-op preschool that my son attended was fantastic but not a good fit for him. There was too much going on—too many sights, sounds, touches, and smells--for him to absorb. A wrote a piece that you might find helpful that describes other preschool options. It's called, “Why Parents Should Choose a Preschool With a Strong Philosophy: Montessori, Waldorf, or Co-op.” https://wehavekids.com/education/Montessori-Waldor...
I believe having play dates is extremely beneficial for autism and social skills. I was persistent and consistent about setting up weekly play dates for my son. He did best with other children one-on-one and usually for a limited amount of time (one hour was about right, and then he'd be drained and want some alone time). My son's interests at that time were very limited (trains, trains, and trains) so I needed to find a youngster who shared that passion with him. I also had to develop a tough skin because other parents didn't reciprocate by inviting my son to their houses. I understood why, but it still hurt.
Lastly, please remember that your journey will be unique to you and your son. Because autism is a spectrum disorder, each youngster is affected so differently. When my son first got diagnosed, some well-meaning people with autistic children told me what to expect and caused me a lot of unnecessary worries (their horror stories didn't come true). Trust your instincts as a mom. Nobody knows your son better than you do. Nobody loves your son more than you do, and nobody wants more for him than you do.