The actress and her husband Dave McCary welcomed their first child together — a baby girl — earlier this month

By Brianne Tracy and Linda MarxLinda Marx

Linda Marx is a writer and reporter for PEOPLE in the areas of entertainment, politics, sports, fashion, travel, design, human interest, lifestyle and art. She has been writing about these topics for more than 20 years.

PEOPLE EDITORIAL GUIDELINES  Published on March 31, 2021 08:00AM EDT

The couple met when Stone hosted SNL in 2016 and a source0 of 1 minute, 3 secondsVolume 0%

Emma Stone is taking on her favourite role yet: mom.

The actress, 32, and her husband, writer-director Dave McCary, welcomed their first child together, a baby girl, earlier this month.

“Emma and Dave have a great marriage and both wanted a child,” a source close to Stone tells PEOPLE in this week’s issue, on newsstands Friday. “They are a very grounded and private couple and were ready for a family.”

Stone first met McCary, 35, on the Saturday Night Live set when she hosted in 2016, and they collaborated on a taped sketch titled “Wells for Boys.” Since then, the couple — who quietly tied the knot in 2020 after getting engaged in December 2019 — have kept their love low-key.

“Emma is close to her family and good friends but not the type to flaunt her personal life,” says the Stone source. “Dave respects that about her and is the same way. They have a great life together and support each other.”

Emma Stone. TODD WILLIAMSON/NBC/GETTY

Two months after Stone subtly hinted last November that she and McCary were expanding their family — “I feel pretty good about starting my own pack,” she told Entertainment Tonight while promoting her film The Croods: A New Age — a source confirmed to PEOPLE that the couple were indeed expecting.

“Emma has been very excited about the baby,” an insider says of Stone, who’s been nesting with McCary in the L.A. area.

“She has been private but said that she was feeling great. She always has a huge smile when she is with Dave.”

Emma Stone and Fiancé Dave McCary ‘Got a Home Together’ This Summer: They’re a ‘Great Match’

Emma Stone and Dave McCary. DAVE MCCARY/INSTAGRAM

As she settles into her new life as a family of three, Stone — who will next appear onscreen as villain Cruella de Vil in the movie Cruella, in theaters and streaming on Disney+ May 28 — is enjoying life as a working mom.

“She is a professional who loves and breathes her work,” says the Stone source. “But if anyone can be good at both, it is Emma. She is a gifted person in every way.”

Dave McCary and Emma Stone. KEVORK DJANSEZIAN/GETTY

Adds a film-world source: “Emma and Dave have a strong and respectful marriage. A baby will add a new dimension of bliss for both of them.”

For all the details on Emma Stone’s baby bliss, pick up the latest issue of PEOPLE, on newsstands everywhere Friday.