The instinct is to send something immediately, and the instinct is right. But the first week is the crowded one. Lilies on every surface, a fridge nobody can close, a house full of people being kind. Then the week after that, everyone goes back to work.
The gifts that land are the ones that arrive later and ask for nothing. No card to write back. No vase to find. No thank-you owed, and no decision required from a person who is currently unable to decide what to have for lunch.