Meghan Markle is loving life as a new mom.
The Duchess of Sussex made her first public outing with 2-month-old Archie at husband Prince Harry and brother-in-law Prince William‘s charity polo match on 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!)
Prince Harry, 34, joined his wife and son following the polo match. The trio walked to the parking lot and shared a sweet moment when both parents smiled at their baby boy, who was now bundled up in a blanket.
Photos of the family of three “showed real life,” the source adds.
Meghan and Harry are focused on giving their son a peaceful start.
“They are basking in the glow and enjoying each day,” a royal source tells 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.”
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Even though the new mom, 37, is a member of the British royal family now, she hasn’t let go of her native California roots. She sported aviator style sunglasses with gold frames with a flowing khaki green dress by Lisa Marie Fernandez — choosing to forego the outfit’s belted bow option. Meghan let her long hair down, contributing to her free spirited vibe.
A friend previously told PEOPLE that Meghan’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.”
William was also joined by wife Kate Middleton and their three kids — Prince George, Princess Charlotte and Prince Louis — at the King Power Royal Charity Polo Day on Wednesday. The match will help raise funds and awareness for charities supported by the royal brothers.
The special event marks the royal cousins’ first public playdate together.