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.