The exact words from the novel are:
"It felt like something was stuck in his throat, making it hard to speak. He wasn't sure. Even though he thought it was impossible, he still harbored a faint hope, a conflict of feelings.
A boy dying from poison, Lee Sa-young who used poison. A boy whose records were erased by Prometheus or some other hand, Lee Sa-young who escaped after being a test subject of Prometheus. A boy who tried to smile with narrowed eyes, Lee Sa-young who smiled with narrowed eyes.
'It can't be.'
Cha Eui-jae looked at Lee Sa-young with confused eyes. At that moment, Lee Sa-young smiled. His eyes narroed, shining like a child's, waiting for the moment to open his prepared gift."
Basically, LSY wanted CEJ to find out his identity at this moment so he laid out an entire scene where CEJ would put the dots together. Especially because he recognized a lot of traits in LSY that the boy had (cuz they're the same person).
It's understandable that it was confusing because what made CEJ realized was a lot of things that culminated when he had the last piece of the puzzle. Also, CEJ already had the boy on his mind so his most desperate wish would be for LSY and the boy to be the same person.

how did he come to that conclusion lmfao the natural conclusion would've been that the experiments were so terrible that he desperately wanted to escape and hence awakened