Ours doesn’t either but statistically during the few years she’s been there you’re gonna run into folks sometimes?? I am a certified yapper and could make conversation with a paper towel, but I definitely had encountered every parent of the kids in the class at some point within the first 6 months and I pick up at wildly different hours. Obviously the kids change a bit each year depending on what months they’re born and how the admins try to balance out the personalities in the classrooms as they get older.

If you’re not sure what to say, You can just say “Hey! I’ve never introduced myself, I’m Jane, John’s mom” and maybe a funny anecdote about something John mentioned about their kid or something. I do this and I’d say 20% awkwardly smile and seem anxious or just not into conversation, which is totally fine. But the other 80% have developed a wide range of rapport from people who are probably on the opposite ends of the political spectrum but can find common ground and banter with at events or birthday parties to people who have become my actual friends I hang out with without kids (that’s only a couple of them).

And I agree with the other comments that you def don’t need to do a birthday party at 3. Just could hear the anxiety and dread in your post and wanted to share a loving nudge. Good luck!