The cast of Star Trek: The Next Generation is reflecting on the franchise's legacy — and what its late creator, Gene Roddenberry, would've thought about Picard — as the Paramount+ series comes to a close.

Speaking to PEOPLE at the Picard finale screening on Thursday — the same day that the series finale dropped on Paramount+ — cast members of TNG say not only did reuniting for the third season of the sequel series deepen their already close bond, the critical acclaim and fan appreciation would've delighted the franchise's creator.

"He'd surely be thrilled, right?" Jonathan Frakes, who plays Will Riker and directs several episodes of the season, says of Roddenberry, who died at age 70 in October 1991 following a series of health complications.

Despite Roddenberry's visionary, optimistic view of the future that informed both the original Star Trek series that launched in 1966 and its TNG follow-up that debuted in 1987, Frakes, 70, says the legendary writer-producer could also see the world — especially that of cutthroat Hollywood — in a harsher light.

"Even as cynical a man as he was, I'm sure he'd be thrilled," the actor notes at the Los Angeles event, where he was joined by his longtime co-stars Patrick Stewart, Brent Spiner, LeVar Burton, Gates McFadden, Michael Dorn and Star Trek: Voyager veteran-turned-Picard regular Jeri Ryan. "And I think we're serving his vision."

"A lot of his principles, of a world where there's no sexism and no racism and no money and people respect each other, I think that's at the core of this whole idea," Frakes adds. "And I think it's part of it's the key to the success of the whole thing."

The bond that the TNG cast shared "was almost immediately deep, and always deep," says Stewart, 82, who plays the spinoff's titular Starfleet admiral Jean-Luc Picard.

"There was a connection that we all made and which was nurtured and encouraged and survived," he explains of the seven seasons of the series and the additional four theatrical films. "I've worked with a lot of companies, groups of actors in plays that ran for a year or in other shows, television shows that have run for more than a year, and nothing has had the impact on my life like this."

Frakes was in agreement. "Unlike some shows, we were a family, we all got this job that sort of changed our lives at the same time," he says. "LeVar was already a big star; Wil Wheaton was a bit of a star; but the rest of us were trying to cobble together our careers and this was this was the career-changing job for all of us. And I think we all appreciate it at the same time. And still do."

Throughout that long, shared history, the central cast — which also includes Marina Sirtis, who plays Deanna Troi, but was unable to attend the screening — has stayed in near-constant contact, through conventions, personal appearances "and just life," says Burton, 66, who plays Geordi LaForge.

But working again as an ensemble two decades after the final TNG film premiered strengthened their bond even further.

"I think it brings us closer together, without a doubt," says Frakes. "There's something about being 20 years older than the last time we were all together that I don't think it just helped me, I think it helped all of us. The characters are deeper… And it was quite thrilling."

"We all felt, 'Wow – pinch ourselves! Is this really happening?'" recalls McFadden, who plays Dr. Beverly Crusher. "That we not only are in each other's lives, but that we can actually be working together."

The cast's legendarily playful off-screen rapport — singing, dancing and joking between takes — returned "immediately," McFadden, 74, says, "because we're all close friends — and that's really genuine. We all know what's happening in each other's lives, pretty much, and so it was a joy to do it."

Adds Spiner, 74, who plays the android officer Data: "I don't think there was any apprehension whatsoever about whether we were all going to have fun together, because we do see each other all the time."

"If we were any closer, it would be obscene," he notes with a laugh. "We're as close as you can get already, so it just laid it in for a little bit more."

Ryan, who plays Seven of Nine, says it was "phenomenal" to watch the TNG cast at work after a long stint as part of the extended Star Trek family.

"I've been friends with all these guys for twenty-something years since I started on 'Voyager,' so I've known them all socially. I've worked with a couple of them as directors over the years on different projects. But to all be on set together and to be actually working together as actors was such a treat and just such a joy," says the actress, 55. "I mean, they're all goofballs and cutups and it was absolute chaos most of the time, but it was so much fun!"

Even though Dorn expected the established chemistry to easily reemerge, the actor, who plays the Klingon officer Worf, says he was still surprised to discover "halfway through the filming, I was having a blast – like a real blast!"

He even found himself reliving warm memories when he watched the penultimate episode, in which the cast reassembled on a revived version of the Bridge of the starship from TNG, Enterprise-D.

"When I saw the Bridge on the screen, that, to me, was a moment, because it transported me back to the first day that I saw the Bridge," recalls Dorn, 70. "I wasn't in makeup, I was just there visiting, basically after a makeup test, and it was this feeling of comfortableness of familiarity. Like your home – your living room or something. And that's what I felt watching at this time. And seeing all of us there, the same thing. It's a real surreal moment."

Burton's 28-year-old daughter Mica — who joined the cast onscreen for the first time, playing Geordi's daughter Alandra — admitted she wasn't prepared to see her father's heartfelt response to reuniting with his old friends.

"Since I've grown up on sets, I've watched him direct. I've watched him act, and I was surprised that he was so emotional, honestly," she shares. "I was honored to be witness to that… I came in ready to work and I got very overwhelmed seeing him burst into tears on our first day at set. Everybody got really emotional, but when you've known somebody for almost 30 years and then they're on set with you, it's a pretty emotional time. So it was pretty cool to see that other side of him."

"It gave us an opportunity to play together on a level that brought back a lot of our youth and I think that it really reaffirmed for us that we don't suck at this," notes Burton, who like the rest of the cast did not rule out future reunions or appearances as their beloved characters, but was utterly satisfied with their latest experience together.

"If nothing else happens after this, I'm good," he adds. "This was unexpected, and a great gift."

Star Trek: Picard season 3 is now streaming on Paramount+.