I'd suggest including the request with the birth announcement to be honest. Something like "<name> has arrived safe and well (insert vital stats if desired) - Mum and bub are doing fine however we would like to spend our first couple of weeks getting to know each other as a family. We will be happy to welcome visitors by arrangement after this time"
I think this is great but I'd ditch the 'however'. You don't have to justify yourself to anyone.

If it was me I'd say something like "We are looking forward to spending the next few weeks getting to know each other as a family. We will have the family over once we get settled. Details to come."




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