Welcome to CAF (Catholic Answers forums)!
I'm also a single mom -- divorced 10+ years and have an annulment.
At my parish I have been so blessed to make good friends among other parents and families. I don't really fit in with the non-parent singles, both because of my age (late 40s) and my ambivalence towards marriage as a future gift from God.
Getting involved in your parish is critical to developing relationships. Not all ministries are created equal in their capacity for meeting and getting to know people. But if you are committed to creating lasting community, take advantage of the opportunities the present themselves.
For example, if you become a lector, introduce yourself to the sacristan and to the parents of the altar servers -- complement their child on something (e.g., so dedicated, attentive, helpful).
Five years ago I got involved in the music ministry. Because I always leave the building after most people (we have to clean up the choir loft after mass), I ended up being around the people who linger outside to chat after mass. At my parish, that's a lot of the homeschooling families, some young families, some older folks with adult children. Some of the singers (there were only 5) introduced me to a couple people, who introduced me to others, and so on.
Incidentally, we have coffee and donuts after mass on Sundays, but sadly that is a terrible place to meet people! At my parish every family and group of friends keeps to themselves. :sad_yes:
Introductions take time to develop into relationships, of course, so be patient and persistent.
And linger after mass on Sunday. When the crowds have thinned, introduce yourself to someone.
Also, daily mass is a great place to meet faithful Catholics.
God bless you and help you find what you need!