It's a good jumping off point, but becoming friends requires time and work.
When we're young, we have nothing but time spent together. As adults, who spend an hour at the local park with some kids, those relationships require more effort to grow.
We have a few friends we've made through our kid, and it definitely takes more work to maintain - but it's been very worth it so far.
> becoming friends requires time, work, and a mutual desire for friendship
FTFY ;-)