Geralt of Rivia (Henry Cavill), star of The Witcher, is himself a Child of Surprise. Played by Cavill, Geralt of Rivia is a force to be reckoned with. Like all the Witchers, Geralt's body was transformed and mutated in order to turn him into an effective killing machine. The most visible sign of Geralt's mutations are his cat-like eyes, which allow him perfect night vision.
But, in truth, Geralt of Rivia seems to stand apart from the rest of the Witchers. There are subtle hints that he is stronger than most, more skilled, more potent. What's more, the hand of destiny rests upon his shoulder. It appears to do so long before he becomes bound to Ciri, the Child of Surprise he initially resisted accepting. The TV series hasn't yet explained that, but it's heavily inspired by Andrzej Sapkowski's novels and short stories, and as a result an important clue is offered in the collection called "The Last Wish."
The Witcher episode 4, "Of Banquets, Bastards and Burials," is a fairly accurate adaptation of Sapkowski's short story "A Question of Price." Just as in the episode, this sees Geralt of Rivia attend a royal banquet that takes a surprising twist when a cursed being named Duny invokes the Law of Surprise for the hand of Princess Pavetta. Years ago, Duny saved the life of King Roegner, who swore to give Duny whatever he found but did not expect when he returned home. When he arrived back at his palace, Roegner learned that his wife was pregnant, meaning the child was destined for Duny. In the TV show, Geralt is unimpressed with the idea of destiny, but in the books he plays a slightly more nuanced role in the drama. He does this because he knows that he too was a Child of Surprise, his life sworn to the Order of Witchers. One of the guests at the banquet, Mousesack, knows Geralt's story, and sums it up.
"He knows this law better than anyone else, because it applied to him once. He was taken from his home because he was what his father hadn't expected to find on his return. Because he was destined for other things. And by the power of destiny he became what he is... A witcher."
A Child of Surprise is a person chosen by destiny itself, and in The Witcher's lore such Children of Surprise are special and rare. This is why Geralt stands apart from the other witchers; he has been chosen by destiny to play this role, and his body was uncommonly tolerant of the mutations, to the extent that the witchers were able to perform experiments upon him that no other witcher has ever been able to survive. Geralt isn't just one of the witchers; he is the Witcher, the best and greatest of them all, possessed of powers beyond any other witcher. What's more, it's fascinating to note that the story of The Witcher sees Geralt cross paths with two other Children of Surprise, one of whom - Ciri - is sworn to him.
It's true that the TV series hasn't developed this idea yet. But, in a sense, it doesn't matter; showrunner Lauren S. Hissrich has clearly chosen to honor Sapkowski's short stories and novels. What's more, The Witcher's season 1 finale ended in such a way as to set up an exploration of Geralt's history, which means it's only a matter of time before the show reveals that Geralt too is a Child of Surprise.