Chris and Katherine Schwarzenegger Pratt are settling into life at home with a newborn.
The actor, 41, and the author, 30, recently welcomed their first child together, daughter Lyla Maria. Chris and Katherine confirmed the arrival of their baby girl on Aug. 10, sharing a photo of them holding hands with their new addition on Instagram.
"We are beyond thrilled to announce the birth of our daughter Lyla Maria Schwarzenegger Pratt," Chris wrote in his announcement. "Both mom and baby are doing great. We feel extremely blessed! Love, Katherine and Chris."
"Everyone is doing well," a source tells PEOPLE. "They haven't left their house since they returned home from the hospital. They just want to bond with the baby and get to know her. They have some help and Maria also makes sure they have everything they need. Lyla is adorable."
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A Baby Girl! Chris Pratt and Katherine Schwarzenegger Welcome Their First Child
"And Kat has the best attitude," the insider adds. "She is obviously still tired, but she loves being a mom. She is so positive and excited about the whole experience. She loves seeing Chris with their girl. He is such a good dad. This was one of the things that Kat was attracted to from the beginning: Chris loves being a dad. Kat feels very lucky that Lyla gets to grow up with Chris as a dad."
A source previously told PEOPLE that the couple "knew they were having a girl and were thrilled about it."
"Kat had a good pregnancy, and she is hoping for a quick recovery — so far, so good," the insider added. "She is going through all the first-time-mom emotions. She is extremely happy but a bit tired and overwhelmed."
Chris, who left the U.K. set of his latest film, Jurassic World: Dominion, to be home for Lyla's birth, has been a steady source of support for Katherine, an author whose most recent book is The Gift of Forgiveness.
"It's comforting for Kat that he is already a dad and understands how it is to have a newborn," the source said of the actor, who is also dad to son Jack, 8 next week, with ex-wife Anna Faris.
In addition to her husband — whom she wed in June 2019 after nearly a year of dating — Katherine has been celebrating with her family, including mom Shriver and dad Arnold Schwarzenegger.
Because Lyla arrived during the ongoing novel coronavirus crisis, the source said, the couple's families weren't able to meet the newborn at the hospital — but "as soon as Kat and the baby got home from the hospital, Maria and Arnold visited. They are both proud grandparents, of course."
For more about Chris and Katherine Schwarzenegger Pratt's life at home with their new baby, pick up the latest issue of PEOPLE, on newsstands Friday.
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