Meghan Markleis loving life as a new mom.

The Duchess of Sussex made her first public outing with 2-month-oldArchieat husband Prince Harry and brother-in-lawPrince William‘scharity polo matchon Wednesday. It was a warm, sunny day, and Meghan mainly stayed under the shade of a tree with her son in her arms.

“She was doting on him, there’s no doubt about that,” an onlooker tells PEOPLE. “She was kissing and stroking him and bouncing him up and down.”

Despite the excitement of the polo match, Archie mainly dozed for his first big outing. Even when he did open his eyes, he was quiet. (Meghan described her son as “really calm”just two days after his birth, and it seems his demeanor hasn’t changed much!)

Samir Hussein/WireImage

Meghan, Duchess of Sussex and Archie Harrison Mountbatten-Windsor attend The King Power Royal Charity Polo Day at Billingbear Polo Club on July 10, 2019 in Wokingham, England

Tim Rooke/Shutterstock

Mandatory Credit: Photo by Tim Rooke/Shutterstock (10331673az) Meghan Duchess of Sussex, Archie Mountbatten-Windsor, Catherine Duchess of Cambridge King Power Royal Charity Polo Day, Billingbear Polo Club, Wokingham, UK - 10 Jul 2019

Kate Middleton, Archie and Meghan Markle.Tim Rooke/Shutterstock

Catherine Duchess of Cambridge, Meghan Duchess of Sussex, Archie Mountbatten-Windsor

Photos of the family of three “showed real life,” the source adds.

Meghan Markle, Prince Harry and Archie.James Whatling/MEGA

Meghan Duchess of Sussex Archie Montbatten-Windsor Prince Harry

Meghan and Harry are focused on giving their son a peaceful start.

“They are basking in the glow and enjoying each day,” a royal sourcetells PEOPLE in this week’s cover story. “As most new parents are, they’re just so excited. There’s something new every day. They’re just really happy.”

Meghan Markle, Archie and Prince Harry.Tim Rooke/Shutterstock

Prince Harry with Meghan Duchess of Sussex and Archie Harrison Mountbatten-Windsor

A friend previously told PEOPLE thatMeghan’s “California roots are coming through” as she prepared to welcome her first child.

“She’s being mindful of what she puts in her body and on her skin and even her at-home cleaning supplies,” the friend added. “She’s hyperaware of what she’s using. She’s looking for natural things.”

Prince George, Meghan Duchess of Sussex, Archie Mountbatten-Windsor

The Duke Of Cambridge And The Duke Of Sussex Take Part In The King Power Royal Charity Polo Day

The special event marks the royal cousins’ first public playdate together.

source: people.com