According to HBO Showrunner Damon Lindelof you can enjoy the show with no prior knowledge of the graphic novels and associated materials (and film), but you'll enjoy it differently, note not better, if you've immersed yourself in the universe before approaching the show.
DL: And I’m very curious how people with no preexisting relationship with the source material process the show versus people who have an intimate relationship with the source material. But at least for the first episode, I imagined two people sitting in a room, one of whom had never seen anything of Watchmen before, including Zack’s movie. Just came in cold. And the person sitting next to them is someone who has read Watchmen a million times and can quote Under the Hood chapter and verse, and will bore you to tears with all their knowledge. My desire was, when the pilot ends, the person who’s never seen Watchmen before turns to the person who is the Watchmen expert and says, “I’m confused, can you explain things to me?” And that person goes, “Nope!” And so they’re like, “Oh, cool, at least we’re in it together.”
Now, as the show goes on, I think if you have an intimate knowledge of the source material, you’re going to appreciate the show on a different level than the people who don’t, but that doesn’t mean you’re going to appreciate it more. I think it will be harder for people who love Watchmen to like the show than it will be for people who don’t love the comic. You can only watch the show through the metric of comparison. It’s called Watchmen, it has characters from the original Watchmen, the creator of the original Watchmen thinks it’s an abomination. These are all barriers to love. I fully embrace that. It won’t be fun — I’m glad I’m not on Twitter — but I knew that when I got in.
‘Nostalgia Is Toxic’: Damon Lindelof on His ‘Watchmen’ Adaptation