Hmm, I actually didn't make many connections through daycare, although I wish you luck. With daycare, everyone is in a hurry to drop off and get to work or pick up and get dinner started. Plus everyone picks up and drops off at different times, so you might never even meet some of the parents. Overall, there isn't a lot of parent interaction IMO. I had more success in making mom friends at kid activities where the parents had sitting-around-waiting time while the kids did the activity. For example, library toddler activities or (once your child is older) soccer/t-ball/etc practices.
If you want to make friends through daycare, then you have to go to extra effort. For example, if your child mentions playing with a particular kid a few times, send a note home through the daycare asking if they would like to meet you and your child at the playground on the weekend to give the kids a chance to play and give them your text info. Then you can make conversation at the playground while you kids play and try to find out if you have anything in common with the parent.
Same idea for library time - if you see a child/mom who looks nice, approach them and ask if they'd like to get together at a park sometime to let the kids play.
I would also encourage you to not limit yourself to moms or to any other particular feature like age because that matters very little now that everyone is an adult (one of my best friends is old enough to be my mom). Pick 1 night a week and sign up for a class that interests you - exercise or art or gardening or whatever. You might meet someone who seems nice, chat in class, and eventually it might morph into a friendship - by the end of the class you might decide hey, let's meet for coffee before or after class next week or something like that. It takes a little more effort but it's the only way to really get to know other adults as an adult.
Good luck!