It depends on the set up, I’m also a lone parent, there has never been a second parent.
I had tried meeting people but it wasn’t work, I didn’t have time etc, so I gave up for a while.
When he was three I signed up to a dating agency (I thought this would be mortifying, but it was fine if a little bit awkward in the initial stages of questions etc as they asked about everything). I wasn’t convinced it would really go anywhere, but a few of my friends persuaded me to do it so I gave it a go.
I went on a date on what was my monthly day off from parenting, he was really really nice and it was my ‘oh shit’ moment as I realised I would struggle to dedicate any time to seeing him again. Really it was me putting barriers in the way, so I begged and persuaded people my son is happy to be with to do the some babysitting and managed to get one evening a week to date, we also sometimes met up during our lunch hour. I know lots of people don’t approve of this but he would sometimes come over once my son was in bed, I had friends over most evenings, so someone being in the flat if he woke up wouldn’t be unusual, although it never happened as he is a good sleeper (and hearing impaired).
It did mean them meeting after the six month mark, as that was the only real way of spending more time today. Then we built up so a few hours at the park became park and then lunch at ours, which then became him coming to ours without meeting outside first etc and then we introduced a sleepover night once a week, this then became twice a week (but not consecutive days), then a little weekend away together. Now we live together and moving in together actually went smoother than I expected.
I did have a huge luxury though, I only work four days a week, so when my son started school my boyfriend changed his study day to coincide with my free day. We would have probably struggled without that as was our own real quality time together.