I find it interesting that everyone believes that K is not “the child”. I think he most definitely is. Or at least, “a child”. Let me explain
So, there was the immunocompromised scientist who is known as the best memory maker. She said that the point of implanting memories is to give the robots positive moments to look back on, so that’s the first thing that debunks the idea that K’s memory of the wooden horse was an implant; no one would implant a memory about a child getting bullied.
But that’s not all. K ended up finding the horse in the same place that he put it in his memory, in the furnace of the orphanage. This means that he grew up in the orphanage, meaning that he was a kid once, and his memory was real.
So, in my opinion, there’s no way he’s NOT the child, as he’s a replicant, and we only know that one exists.
But here’s another thing: the person who the characters accept as the child, the scientist, is immunocompromised. Now how the heck could a robot get sick? It couldn’t.
My opinion is that they used the scientist as a cover; calling a real human “the child”, and telling everyone that, behaving as such, and then placing the real child in an orphanage with sketchy record-keeping processes means that only one person truly knows that the immunocompromised woman isn’t the child, and since she’s shut in and no one is allowed to interact with her in person/physically, very few people would even know whether or not she’s a replicant.
The other alternative is that K is the child of another two replicants. I actually think that the Tyrell company was secretly designing replicants that could reproduce independently but that feature didn’t work properly or reliably, explaining why the child could have been created in the first place. This could open the door for other children to exist in the universe, although they would bee extremely rare and hard to find. But still, there’s the immunocompromised plot hole.