June 04, 2014 08:30 PM

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Update: The couple have named their son Oliver Finlay Dallas, PEOPLE confirms via the birth certificate. TMZ was first to report the news.

Originally posted May 30: Is Ginnifer Goodwin the fairest mom of them all?

The Once Upon a Time actress and her husband, costar Josh Dallas, welcomed their first child — a boy! — on Thursday, May 29 in Los Angeles, her rep confirms to PEOPLE exclusively.

“Thanks for all the well wishes about our new baby boy,” Dallas, 32, Tweeted Tuesday. “We are in LOVE! He’s our favorite person.”

“Both mom and baby are doing great,” their rep tells PEOPLE.

The couple have not yet released the name of their son, although Goodwin, 36, has said they’ve put a lot of thought into choosing it.

“Naming a child with the last name of ‘Dallas,’ is a little more complicated,” she said last month — but the couple have definitely been doing their research.

“We read so many books. I can’t even tell you. I could probably teach a college-level course in bringing up a child,” Dallas joked recently. “It doesn’t mean I’ll be great at it, but I hope I’m good at it.”

The couple — who play Snow White and Prince Charming on the hit series — are quickly finding their own happily ever after. Weeks before Goodwin and Dallas, 32, confirmed the pregnancy, they announced their engagement and were married in an intimate ceremony on April 12.

“It hit me like a blinding light. I thought, ‘I’m in trouble now,'” Dallas has said of falling for the actress.

— Anya Leon with reporting by Julie Jordan

Video Flashback: What Josh Dallas Thinks of His Costar (and Wife!) Ginnifer Goodwin?

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