Uma Thurman -- Shows Off New Baby ... One Day After Birth!

Just one day after giving birth, supermom Uma Thurman was already out and about in public holding her newborn daughter at a cafe in upstate New York.

With her one-day-old bundle of joy safely in her arms, the 42-year-old was spotted at Press and Blend in Woodstock, New York. We're told Uma is a regular at the shop and ordered cold pressed juices. A new mom needs her nourishment!

On Sunday, Uma gave birth to her first child -- whose name has yet to be announced -- with boyfriend Arpad Busson. She has two children with ex-husband Ethan Hawke, while Arpad has two children from his previous relationship with supermodel Elle Macpherson.