notanan It doesn't have to be a play group, a mother and toddler group is just as good.
There are core instinctive relationship skills that a child picks up by being part of a small community of similar aged children. Transient social occasions in parks, shops etc are not at all the same thing.
I had plenty of those kind of opportunities. What I lacked was mixing regularly with the same group other children, learning to attune to how people socialised with each other, and most importantly, built and sustained friendships.
You clearly have no conception of what it is like to go to school and suddenly find your self completely lost in a large group of children, a situation I had never been in before. These children seem comfortable socialising, striking friendships, even transient frienships and moving around each other. While I didn't have clue, what to do or what to say,
I made absolutely sure that my children had opportunities to mix and play with children from a very young age, first with friends with similarly aged children, then play group and mother and toddler groups. The result is that both my children have all that comfort in the presence of other people that I never had and have benefitted immeasurably from being at ease in almost any situation.