Camila Alves and Matthew McConaughey
's mom Kay says her son is ecstatic over the arrival of his son.
"Oh my gosh, he's like over the moon," she tells PEOPLE.
Born July 7 in L.A., Levi Alves McConaughey is the first child for McConaughey, 38, and girlfriend Camila Alves, 25, a model and handbag designer.
Was Matthew squeamish in the delivery room? "Oh no! He was nervous but he was just rooting for [Camila] all the time," says the grandma. "He's so proud of how brave and strong she was."
"MaMac," as Kay's other grandchildren call her, hasn't seen any photos of Levi yet, "but Matthew says he has curly dark hair like Camila – and of course he has that beautiful olive skin both of them have."
It's likely the inherited traits won't end there. "Can't you just see that little boy following his dad on the beach in Malibu with a surf board over his head going, 'I'm right behind you, Papa!' " Kay says with a laugh. "That little boy's not going to need anything. He's not going to wear anything but a bathing suit – and maybe not even that!"
Most importantly, "I hope he has Matthew's love for life," adds Kay. "Matthew and Camila are going to make sure that baby learns a lot about life and love."
As for the future, Kay "absolutely" sees more babies for the couple: "I don't think they'll ever quit with one."
Any talk of marriage "would only take away the beauty of what's going on right now," says the proud grandmother. "I've seen people who are married that don't love each other as much as those two people do."