I didn't know asking for hand me downs is a thing in first world countries too.
Well, we offered. It is quite normal to pass things along to friends and family here. Also, there is a massive flea market culture in Finland. And like you said about they grow fast, for babies, they don't really move so the baby clothes are generally in very good condition second-hand. We bought a lot of flea market stuff too. Buying some stuff new is also good though, because it is good to have "memory" items.
That makes a lot of sense.