When your kids are tiny, it's super hard to imagine them being at a party or playing at someone's house without you.
But from year 1 or second term of reception depending on school culture, that's totally normal.
And as they get older, it's more than they say "can Jamie come round?" or "Oliver wants me to go round to play" than you organise and facilitate their playdates/social lives with parents you want to be friends with
Oliver's mum may not be someone you would choose to be friends with but as long as you don't feel like your child is likely to come to serious harm, off they go to play at his house.
I'd honestly not worry that much about your kids moving schools and making friends at infant school age.
You could join the PTA but you could also do other non-school related things to make friends yourself, join a sports club, etc. Maybe the kids will get into a sport or hobby club like Cubs/Brownies and you can volunteer to help out there and build up some network of people
It's not all about school parents for your own network.