Can we explain the mystery of existence? Before trying to answer the question, I would ask first, whether the question is a valid one to be answered.
When asking "why" questions, it is normally between human beings and their dispositions in their own daily lives, such as why have you ordered the book? Because I wanted to learn more about Logic. Why did you wake up earlier than usual this morning? Because I was hungry. ....etc etc, or their explanations to what has happened in the world, but the world must be where the replier had been in his / her life, experiencing the happenings, witnessing the situations etc. Why do you think the team lost the game? Because the players were suffering from fatigues, I guess ...etc etc.
But the OP's questions why human beings exist at all, and any forms of life exist, = this question is out of the boundary a living human being's experience, because no one right now has lived more than 100 years to have directly experienced the very beginning of life of humans or anything form of lives which could be millions of years ago.
Hence, answers will come from each person's imaginations, beliefs or the religious scripts or scientific theories, or some other philosophical systems he read.