Hi olaybiscuitbarrel
I have been there with both DD1 & DD2 (now Y6 & Y4 - and more from the point of trying to get 'names' - which neither really managed until around Christmas Year R). I think you should try to accept they're so young that many are still playing alongside each other, rather than being 'friends'.
Friendship is a gradual thing that relies on shared experience, similar likes/ dislikes and requires a good deal of time to come about.
My advice is see this as a slow process and one which truly won't settle out until late Year 1, even Year 2.
Things to help things along:
Play dates (invite a child over at the weekend or arrange to meet in the park, etc...).
Birthday parties (doesn't have to be extravagant - but throw a birthday party - kids are happy playing old fashioned party games, watching a movie and eating pizza).
Encouraging your DC to share, play nicely and include others.
The single most important thing you can do is smile & say hello in the mornings. If you're the friendly parent who's pleasant to talk to, odds are other parents will form a good impression and that will feed into your child being invited to things.
It's very early days - you're DC has only been in school for about a month - so please don't make any judgements about their success or failure in making friends (especially if they're a new 4 year old).
Try to encourage your child to see many children as friends rather than plum for just one specific BFF. Our DD2 has a great friend who's been her BFF since YR, but her family will be moving away in a few months - DD2 is absolutely devastated, but I have been trying to prepare her for the fact that this is coming and ensuring that she says can see that she has many other friends to play with in her class & outside school.
HTH