I wish I had a friend that had a DD the same age as mine. Then my social life would mix in with hers. But that never happened.
I am an introvert.
I was shy - which is where the social anxiety stemmed from.
Being an introvert for me means I prefer spending time alone or at home (great with adjusting to parenting as I would rather be at home anyway) and I have very small friendship circles - prefer meaningful conversations as I really struggle to gain anything from small talk or maintain superficial relationships.
However my shy trait (which I’ve had since childhood but have grown out of - but that creeps in every now and then) - often means that I might not engage in a conversation because I’m second guessing myself and I won’t always make the first move when it comes to speaking with strangers - but I have forced myself to do this.
I’m stating the difference as both have been good and bad.
My DD actually developed her own social anxiety - selective mutism, until she was about 4/5 which made it so hard for her to make friends.
10 years later she is an only child with her own friendship circle. She aLao sees some of my friends as her friends and she told me “I have so many adult friends.”. She is so confident speaking to adults and where appropriate gets involved in some of our conversations - as at home we are her friends. When she was younger and I was concerned I spoke directly to the teachers when I was worried about her social as well as academic development.
I would say join groups and speak to the parent that your DC is bonding with the most. That way it isn’t about you - it’s about them. Play dates will naturally happen based on that. If it doesn’t then just make the first move.
We spent lots of time at the park, at soft play. We didn’t always invite the same people but my DD always made a friends (even though sadly she never saw many of them again - I’m sure if I was more social I could have taken the parents details).
It is easier to bond with parents at school but mainly through birthday party invites or hanging out at the school gates (I never did the latter) and following up on those relationships - and also get to know DCs friends and their parents.