It's literally as simple as paying for a babysitter. I don't get the defeatist attitude that "I can't pay for a babysitter every time I want to go out on a date for 18yrs" because that's actually nonsense. They suggests you can only ever socialise outside of your house. And my son's father has never had him either, so that's not a total barrier, unless you want to make it one.
I met DH, on a night out, having paid for a babysitter and going out with my friend, no intention of meeting anyone.
I paid for maybe 6 more evenings over a course of time, and then (when I knew him better, and had stalked on social media to look for any red flags) I would invite him round and we'd have dinner when DS was in bed.
Then, gradually he'd pop over in the day, with DS here. Which is absolutely no different to one of my friends popping in, male or female. DS is used to my friends stopping by all the time, my guy friends were always using my garage to tinker on their cars, and would be around a lot. My female friends would often come over for movie nights and stay over. DH was no different in DS mind.
It became so normal for DH to be around, that it wasn't weird when we became an item romantically in DS' eyes. He was chuffed. He was a big fan of DH and his Lego skills lol.
We've been married 4yrs now, with 2dc together.
My friend is constantly complaining about being single. Identical situation to me at the time, one DS and absent father. But if you suggest she gets off her arse and stops whining and actually doing something proactive, all the excuses come out. How she can't possibly leave DC with a random stranger babysitter. Then when I point out, I interviewed over 10 candidates for my babysitter post, and settled with one who was a qualified nursery nurse, two excellent references, DBS checked and with a first aid certificate, so probably better at looking after my child than I was...then the excuse changed to how it was too expensive. Then it was she has nothing to wear. Then it was the fathers fault because he should be having his son and unless he was, it was impossible for her to leave the house and meet someone. And what it boils down to, is that if you want to make it happen, you will, and if you don't, you'll always have an excuse.
Sure it's easier if you've got an ex/parents/friends/family who can have your DC while you initially date. But it's by no means impossible if you don't have that. Just depends on your mindset. It will always be impossible to my friend.