Hugh Hefner's Son Marston and Wife Welcome First Baby, Son Forrest: 'Very Fortunate' (Exclusive)

"I always wanted to be a parent," the 33-year-old son of the late Hugh Hefner tells PEOPLE exclusively

Marston Hefner is a new dad!

The late Hugh Hefner's son, 33, and wife Anna Lambropoulos Hefner are embracing parenthood after welcoming their first baby.

Son Forrest Glenn Hefner was born on Saturday, July 15, the couple confirms to PEOPLE exclusively.

"I always wanted to be a parent, and I just never found the person who felt right for me or who wanted to do it with me, for the long term," the writer tells PEOPLE. "Now, it feels like I'm really in that Hollywood romance stage of things."

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The new mom, also 33, says that before meeting the Los Angeles native, "I always wanted to be married and have a family."

"But dating in Los Angeles is kind of horrifying," Anna, originally from Chicago, notes. "Once I met Marston, I knew. And we've never spent time apart since."

The newlyweds, who will celebrate one year of marriage next month, admit that they were taken a bit by surprise at how quickly their efforts to start a family were successful.

"We knew we wanted children and I thought it would take longer since all kinds of things can happen when you plan to have a family," Anna tells PEOPLE. "But we got very fortunate and we were able to conceive right away, so I've been pregnant most of our newlywed year."

"We got to live the best bachelor life for as long as we possibly could, and then we were like, 'Okay let's have a baby,' " Marston shares.

"We're very fortunate we had an easy pregnancy, easy labor and delivery. So just very grateful that everything went smoothly," Anna adds. "But I was in shock, and Marston really calmed me down and reminded me what a good team we are and that this is what we wanted."

The couple is looking forward to teaching baby Forrest, but also learning about who he is and his own personality.

"We're both out-of-the-box thinkers. We both encourage each other to follow our passions and our joy, and we're respectful of each other being different people," Marston explains. "I think that we're going to embrace Forrest for who he is, and not who we want him to be."

"If he likes Roblox, hey, I'm gonna like Roblox. If he likes basketball, I'll like basketball. I'm not going to say, 'You should be a soccer player for us,' and I think we both see eye to eye on that one."

Marston jokes he's more of a "hippie" while Anna admits she "tends to run a little more anxious."

"I think it's important for kids to be interested in something but also to develop a passion that they enjoy focusing on," she shares. "But I think Marston and I are aligned on the big things. As long as he feels supported and he feels he can express himself to be whoever he wants to be, that's the most important thing."

When it comes to supporting one another, Marston says he and Anna wanted to "process [the experience] in our authentic way."

"Little things made a difference. Genuinely feeling all the feelings we were feeling, the highs and the lows, and being honest about, 'This is tough right now' or 'This is amazing right now.' So then when it came to that nine-month mark, we felt really ready."

Anna adds, "Like many women, I had anxiety about being pregnant and becoming a new mom and I feel like Marston was so zenlike and supportive. He fave me a safe space to feel whatever I was feeling and to know that he had my back."

"For me, I love exploring whenever I am. I'm restless, I don't like being cooped up in the house, but Marston is more of a homebody, which is okay. That's him. I felt very supported though because knowing how much I like to go out — I'm a foodie and love trying out new restaurants — he definitely came out of his shell a little bit more to make sure I felt like I was able to get out and enjoy things."

Marston says one of the biggest changes in fatherhood so far is spending less time with his previous favorite hobby, gaming. "I'm a big gamer and there was just something that happened naturally where I was like, 'I'm going to miss out.' "

"I'm gonna miss out on being there for my son. I'm gonna miss out on being there for Anna and I don't want to be the dad where this is a sideshow thing. I want to be present. This is family time now and time to spend more time together, whether that's going to the farmer's market or dinner."

Though they come from different backgrounds, Marston and Anna both agree that when it comes to raising their kids, "screw the conventional."

"I grew up having the least conventional relationship with the world and I feel really grateful," Marston says. "I enjoy my life. I feel really grateful for the life that my dad gave me. So with Forrest, I don't care how other people are doing it. I want us to do what we think is best. Let's make the sweetest, most curious human being that we can. That's my priority."

"I also had very untraditional parents, so I think that's kind of a margin we could connect on," Anna says. "Our parents were very free-thinking and really encouraged that in us, and I think we'll carry that way of being as we raise Forrest."

While he doesn't have the extensive archive his late father was proud to maintain of his own life, Marston says that going through those mementos of his dad's as a young adult helped strengthen their bond.

"My internship in college was to work in his scrapbook room and I used it as a way to get to know him," he recalls. "He was scrapbooking from elementary school. He had comics of himself, documenting his life as if he was the main character."

"I keep journals, I keep diaries. My writing is like that. I've written for 12 or 13 years and that's the continuous thing that makes me a sane person."

Now that Forrest has been introduced to the world, Marston and Anna feel it's important to keep his life quiet and private.

"I'm not going to put him on my social media," Marston says. "It's just that it's his life and I don't want him to feel like he's just part of my thing. He's going to want to do his own thing and if that includes social media, cool. If not, also cool. I don't want to make that choice for him."

Aside from the many firsts ahead of them, the couple is looking forward to dressing their little guy up for his first Halloween and getting into the rhythm of their family.

"I'm looking forward to getting a little more sleep," Anna laughs.

"It's all the little things, just seeing him develop and getting some home videos of him as he does," Marston says. "I don't want to forget what it's like because it happens really quickly."

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