On the first day? Barely, though in "good" daycares, you usually have a connection because placement is competitive and you got in through nepotism.

After a couple months? If you don't know the other kids by name and some other parents, you may have a bad daycare full of people who do not care.

My sister ran a fairly renowned daycare for over a decade. She ended up the caretaker for the children of many friends, and gained many friends of the children she helped raise. The daycare was a massive part of their community. It allowed the parents to function in modern society while ensuring their child was in the care of, essentially, an expert.

How well does the average person know their neighbors when they move to a new place? Maybe if you had a routine where you and your children meet other families that live close to you... hmmmm

I'm not a parent but my niece and nephew (different parents) both go to daycare. My sister knew many of the parents at her son's daycare already, they live in the same neighbourhood. My nephew knew the children of those parents too. He had his little daycare friends before he started daycare at 18mo. My sister has lived in the same city all her life, some of the parents involved she's known for 30 years.

I'm not as close to my sister in law as I am my sister, but I know that when my niece started daycare they knew some kids and parents from the playground already.

It doesn't strike me as bizarre that someone would know people in their community who are in a similar life stage.