I’ve largely had the same experience with all my three.
You just have to persevere. I have met two great friends, long lasting over the years, but that was after going to countless groups and really getting stuck in, inviting people over, asking if they wanted to meet at the park.
I met a great group of people like that 20 odd years ago when my first was a toddler, and with my second who is now 11. Sadly, a lot of those friendships didn’t last the years due to me moving around the country and just life, but I’m still in touch with some.
My youngest is 4, and I’m old and tired now so didn’t try so hard, but still made an effort and have a couple of people here now, through her playgroups and my older DDs school.
My only tip is to be really friendly and take the plunge and ask people to do stuff. Not everyone will like you, and you won’t like everyone but you may be lucky and find a couple of people you click with, and having kids the same age is just incidental.
Its easy for me though as I give no shits, I will talk to anyone and I’m not shy at all and I love hosting, I can see how it would be harder if you weren’t like that.
When mine were little, I emailed and called all the local churches to find out about what groups were run from their halls.