Warning: SPOILERS about The Rings of Power episodes 1 and 2 ahead.The Rings of Power is set in the Second Age before the creation of the Rings of Power, the absence of someone in particular can be noted.
The Rings of Power episode 1's beginning firmly placed Galadriel among the show's protagonists, slowly introducing the other main players as well, but making Galadriel out to be the one most intent on finding and defeating Sauron. Indeed, Galadriel's determination in wanting to extinguish the threat of Sauron is shown as deeply intertwined with the trauma of losing her big brother Finrod to him, causing her to take the mantle of his mission to find and defeat "Morgoth's most devoted servant." Hell-bent on the belief of Sauron still being a threat despite the time of apparent peace in Middle-earth, Galadriel is proved right by The Rings of Power episode 2. Still, Galadriel's certainty in her beliefs leaves her somewhat isolated by her Elven peers, painting a picture of a headstrong but ultimately isolated Galadriel.
While The Rings of Power's Galadriel is alone, she shouldn't be, as The Silmarillion – partially the source material for The Rings of Power – described Galadriel meeting her future husband Celeborn during the First Age. So not only should they be already married by the start of the Second Age, but around the year 300 of the Second Age, they should have also had their daughter, Celebrían. It's unclear why Galadriel is shown to be unmarried during the Second Age in The Rings of Power, but Amazon's TV show might just be playing the timeline, being set on showing Galadriel's family, but further down the line, willing to let her mission play out beforehand.
Galadriel's Husband & Children In Lord Of The Rings
As millennia between the two stories, it isn't just The Rings of Power's Galadriel's age that differs from Lord of the Rings. Although the books go further than Peter Jackson's Lord of the Rings movies in telling Galadriel's backstory, Lord of the Rings: The Fellowship of the Ring introduces Galadriel's husband, Celeborn (Marton Csokas), as he meets the fellowship right after Gandalf the Grey is presumed slain by the Balrog. Although unseen in the films, Celeborn and Galadriel also have a daughter, Celebrían. Galadriel's daughter eventually marries Galadriel's long-time friend Elrond and has three children with him, the two twins, Elladan and Elrohir, and Arwen.
It's unclear if and when Galadriel's husband and child will be introduced to The Rings of Power. As they were already made known in Peter Jackson's Lord of the Rings movies, though, they will likely be. Hopefully, it'll happen in The Rings of Power season 2, whose filming will begin soon in the UK.
New Episodes of The Lord of the Rings: The Rings of Power release every Friday on Amazon Prime Video.