I don't think children this age really socialize. If I remember correctly, its still mostly parallel play, or maybe curiosity and mimicing, but not much give and take interaction. Since he does well with family I wouldn't force the issue; there are numerous reasons he might not be comfortable engaging other kids on the playground. If it becomes clear he WANTS to, but doesn't know how, then you can intervene for him: "I see you are having fun scooping the sand. My son, Z, likes to do that, too. Why don't you two play together?" At this age parents still do most of the facilitating and most "friendships" are still determined by the parent's friendships.
Play groups are good for toddlers because they have the opportunity to get comfortable with a set and limited group of children, if you don't think your son would find it too overwhelming. My son always enjoyed his playgroup.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).