As for things like “singles’ groups”. Many churches of any size will have a young adults group (18-30, more or less) and these often attract the 30-plus singles. Partly because one is more likely to “find someone”, especially in a large church, but there are other reasons.
What also happens, I have observed, is that there is a lot of informal mentoring; with the older single men helping the younger ones (I benefitted a lot from the help of one man who didn’t marry until past 40), and the older single women doing likewise for the younger women. The church I belong to does offer a formal programme to encourage mentoring (discipling) of this sort.
We love having our kids with us for part or all of service but also do not think it’s something to be dogmatic about. In times where I have been alone (my husband working out of town or serving elsewhere in the church), frazzled or just very tired myself it has been a blessing to take my toddlers to church nursery where someone will love them, care for them, and even teach them about Jesus, so that I can fully enter into corporate worship — without needing to discipline, diaper or direct small people. I homeschool and am with my children almost constantly, so I’m very adept at worshipping alongside them— we have family worship as well as daily devotions — so it’s not that I want to deny them a chance to see adults worshipping or worship with me. It’s that I’m just one woman and there are 3 of them (or more, we have been foster parents too) and sometimes I don’t have the mental space to both parent and listen/pray/etc.
I re-iterate that our norm is to have our infants and older kids (3&up) sit with us for most of if not all of any service we are a part of… but I also appreciate the option to share responsibilities when it comes to my toddlers (whom I don’t want to teach that church is a place for eating, distracting oneself and sleeping— ie how we keep toddlers quiet in church), and I can understand how parents could want a nursery and find it helpful!
As the Apostle Paul said, don’t let anyone judge you with regard to new moons, sabbaths, eating meat, and nurseries. Have faith and do as you please. And if you get criticized by other mothers who are your peers, consider yourself successful in practicing Christian liberty. Love,